fun = @(x) 10*exp(-50*abs(x)) - 0.01./((x-0.5).^2+0.001) + 5*sin(5*x);
tol = 1e-10;
I = quadl(fun,-1.00,1.00,tol,0.1);
I
18 -1.0000000000 1.00000000e+00 3.3925340851
23 -1.0000000000 9.17517095e-02 0.8718022692
28 -1.0000000000 8.41837620e-03 0.0815594420
33 -0.9831632476 1.69411726e-02 0.1678605716
38 -0.9492809024 2.05163060e-02 0.2041212474
43 -0.9082482905 2.05163060e-02 0.1969654986
48 -0.8672156785 1.69411726e-02 0.1513581363
53 -0.8333333333 8.41837620e-03 0.0699373733
58 -0.8164965809 1.84641493e-01 0.0252451108
63 -0.8164965809 1.69411726e-02 0.1276112302
68 -0.7826142357 3.40924808e-02 0.1914166871
73 -0.7144292740 4.12870929e-02 0.0905085863
78 -0.7144292740 3.78816136e-03 0.0151034166
83 -0.7068529513 7.62331047e-03 0.0263537668
88 -0.6916063304 9.23207464e-03 0.0245088942
93 -0.6731421811 9.23207464e-03 0.0162006159
98 -0.6546780319 7.62331047e-03 0.0070136257
103 -0.6394314109 3.78816136e-03 0.0013282672
108 -0.6318550882 4.12870929e-02 -0.0776142111
113 -0.6318550882 3.78816136e-03 -0.0001071441
118 -0.6242787655 7.62331047e-03 -0.0045641493
123 -0.6090321446 9.23207464e-03 -0.0132675405
128 -0.5905679953 9.23207464e-03 -0.0216385871
133 -0.5721038460 7.62331047e-03 -0.0240504124
138 -0.5568572251 3.78816136e-03 -0.0139863777
143 -0.5492809024 3.40924808e-02 -0.1825018883
148 -0.4810959407 1.69411726e-02 -0.1241752934
153 -0.4472135955 2.23606798e-01 -1.4231257287
158 -0.4472135955 2.05163060e-02 -0.1737049541
163 -0.4061809836 4.12870929e-02 -0.3979302010
168 -0.4061809836 3.78816136e-03 -0.0343454657
173 -0.3986046609 7.62331047e-03 -0.0708528810
178 -0.3833580399 9.23207464e-03 -0.0884119557
183 -0.3648938907 9.23207464e-03 -0.0905599231
188 -0.3464297414 7.62331047e-03 -0.0758530390
193 -0.3311831205 3.78816136e-03 -0.0379069365
198 -0.3236067977 5.00000000e-02 -0.4863436541
203 -0.3236067977 4.58758548e-03 -0.0459948603
208 -0.3144316268 9.23207464e-03 -0.0924797145
213 -0.2959674775 1.11803399e-02 -0.1109046718
218 -0.2736067977 1.11803399e-02 -0.1084113227
223 -0.2512461180 9.23207464e-03 -0.0866821195
228 -0.2327819687 4.58758548e-03 -0.0418709654
233 -0.2236067977 5.00000000e-02 -0.3793679874
238 -0.2236067977 4.58758548e-03 -0.0409542998
243 -0.2144316268 9.23207464e-03 -0.0792914980
248 -0.1959674775 1.11803399e-02 -0.0896234733
253 -0.1736067977 1.11803399e-02 -0.0815383091
258 -0.1512461180 9.23207464e-03 -0.0604505884
263 -0.1327819687 4.58758548e-03 -0.0275098189
268 -0.1236067977 4.12870929e-02 -0.1411576318
273 -0.1236067977 3.78816136e-03 -0.0213659915
278 -0.1160304750 7.62331047e-03 -0.0390373348
283 -0.1007838541 9.23207464e-03 -0.0393457303
288 -0.1007838541 8.47058630e-04 -0.0039910480
293 -0.0990897368 1.70462404e-03 -0.0078091768
298 -0.0956804888 2.06435465e-03 -0.0090470325
303 -0.0915517795 2.06435465e-03 -0.0085784763
308 -0.0874230702 1.70462404e-03 -0.0067135501
313 -0.0840138221 8.47058630e-04 -0.0032064466
318 -0.0823197048 9.23207464e-03 -0.0285909660
323 -0.0823197048 8.47058630e-04 -0.0031175587
328 -0.0806255876 1.70462404e-03 -0.0059948188
333 -0.0772163395 2.06435465e-03 -0.0067347194
338 -0.0730876302 2.06435465e-03 -0.0061171768
343 -0.0689589209 1.70462404e-03 -0.0045478671
348 -0.0655496728 8.47058630e-04 -0.0020788252
353 -0.0638555556 7.62331047e-03 -0.0122507130
358 -0.0638555556 6.99451768e-04 -0.0016212527
363 -0.0624566520 1.40757942e-03 -0.0029882153
368 -0.0596414932 1.70462404e-03 -0.0030942763
373 -0.0562322451 1.70462404e-03 -0.0024662971
378 -0.0528229970 1.40757942e-03 -0.0015163769
383 -0.0500078382 6.99451768e-04 -0.0005642947
388 -0.0486089346 3.78816136e-03 -0.0005668980
393 -0.0410326119 2.05163060e-02 0.1518115181
398 -0.0410326119 1.88240614e-03 0.0015337661
403 -0.0372677996 3.78816136e-03 0.0077139663
408 -0.0296914769 4.58758548e-03 0.0203067573
413 -0.0205163060 4.58758548e-03 0.0377446944
418 -0.0205163060 4.20918810e-04 0.0026292180
423 -0.0196744683 8.47058630e-04 0.0057516868
428 -0.0179803511 1.02581530e-03 0.0078477353
433 -0.0159287205 1.02581530e-03 0.0089018859
438 -0.0138770899 8.47058630e-04 0.0082178472
443 -0.0121829726 4.20918810e-04 0.0043963212
448 -0.0113411350 3.78816136e-03 0.0505214482
453 -0.0037648123 1.88240614e-03 0.0339908857
458 0.0000000000 2.23606798e-01 1.6698194082
463 0.0000000000 2.05163060e-02 0.1934869262
468 0.0000000000 1.88240614e-03 0.0343429706
473 0.0037648123 3.78816136e-03 0.0533636092
478 0.0113411350 4.58758548e-03 0.0449972715
483 0.0113411350 4.20918810e-04 0.0048879757
488 0.0121829726 8.47058630e-04 0.0093137662
493 0.0138770899 1.02581530e-03 0.0104195043
498 0.0159287205 1.02581530e-03 0.0095737998
503 0.0179803511 8.47058630e-04 0.0073339657
508 0.0196744683 4.20918810e-04 0.0034682599
513 0.0205163060 4.58758548e-03 0.0317186595
518 0.0296914769 3.78816136e-03 0.0202554383
523 0.0372677996 1.88240614e-03 0.0088089771
528 0.0410326119 4.12870929e-02 0.1845476092
533 0.0410326119 3.78816136e-03 0.0161596184
538 0.0486089346 7.62331047e-03 0.0297648303
543 0.0486089346 6.99451768e-04 0.0028274249
548 0.0500078382 1.40757942e-03 0.0055943147
553 0.0528229970 1.70462404e-03 0.0066533501
558 0.0562322451 1.70462404e-03 0.0065797110
563 0.0596414932 1.40757942e-03 0.0054158300
568 0.0624566520 6.99451768e-04 0.0026941996
573 0.0638555556 9.23207464e-03 0.0369214169
578 0.0638555556 8.47058630e-04 0.0032707681
583 0.0655496728 1.70462404e-03 0.0066260190
588 0.0689589209 2.06435465e-03 0.0081411518
593 0.0730876302 2.06435465e-03 0.0083134776
598 0.0772163395 1.70462404e-03 0.0070218699
603 0.0806255876 8.47058630e-04 0.0035481305
608 0.0823197048 9.23207464e-03 0.0416510892
613 0.0823197048 8.47058630e-04 0.0035896908
618 0.0840138221 1.70462404e-03 0.0073563938
623 0.0874230702 2.06435465e-03 0.0091592461
628 0.0915517795 2.06435465e-03 0.0094486432
633 0.0956804888 1.70462404e-03 0.0080291093
638 0.0990897368 8.47058630e-04 0.0040680060
643 0.1007838541 7.62331047e-03 0.0390207030
648 0.1160304750 3.78816136e-03 0.0210299496
653 0.1236067977 5.00000000e-02 0.3684611645
658 0.1236067977 4.58758548e-03 0.0269234520
663 0.1327819687 9.23207464e-03 0.0588884742
668 0.1512461180 1.11803399e-02 0.0792224140
673 0.1736067977 1.11803399e-02 0.0869624536
678 0.1959674775 9.23207464e-03 0.0768318693
683 0.2144316268 4.58758548e-03 0.0396325012
688 0.2236067977 5.00000000e-02 0.4646021421
693 0.2236067977 4.58758548e-03 0.0404746245
698 0.2327819687 9.23207464e-03 0.0836129301
703 0.2512461180 1.11803399e-02 0.1041270857
708 0.2736067977 1.11803399e-02 0.1058045096
713 0.2959674775 9.23207464e-03 0.0874445639
718 0.3144316268 4.58758548e-03 0.0431384283
723 0.3236067977 4.12870929e-02 0.3501146453
728 0.3236067977 3.78816136e-03 0.0353348952
733 0.3311831205 7.62331047e-03 0.0699746788
738 0.3464297414 9.23207464e-03 0.0818201603
743 0.3648938907 9.23207464e-03 0.0771576296
748 0.3833580399 7.62331047e-03 0.0587802479
753 0.3986046609 3.78816136e-03 0.0270470338
758 0.4061809836 2.05163060e-02 0.1053543582
763 0.4061809836 1.88240614e-03 0.0128025485
768 0.4099457959 3.78816136e-03 0.0242931985
773 0.4175221186 4.58758548e-03 0.0263357768
778 0.4266972895 4.58758548e-03 0.0221471091
783 0.4358724605 3.78816136e-03 0.0143017540
788 0.4434487832 1.88240614e-03 0.0054739713
793 0.4472135955 1.84641493e-01 -0.7527601574
798 0.4472135955 1.69411726e-02 -0.0318555571
803 0.4472135955 1.55438155e-03 0.0035738480
808 0.4503223586 3.12804340e-03 0.0042047151
813 0.4565784454 3.78816136e-03 -0.0013492140
818 0.4565784454 3.47570280e-04 0.0001925751
823 0.4572735860 6.99451768e-04 0.0002053257
828 0.4586724895 8.47058630e-04 -0.0000911353
833 0.4603666068 8.47058630e-04 -0.0004833469
838 0.4620607240 6.99451768e-04 -0.0007104922
843 0.4634596275 3.47570280e-04 -0.0004621403
848 0.4641547681 3.78816136e-03 -0.0102326253
853 0.4641547681 3.47570280e-04 -0.0005367323
858 0.4648499087 6.99451768e-04 -0.0013129179
863 0.4662488122 8.47058630e-04 -0.0020229428
868 0.4679429295 8.47058630e-04 -0.0025204045
873 0.4696370467 6.99451768e-04 -0.0024737166
878 0.4710359503 3.47570280e-04 -0.0013659112
883 0.4717310908 3.12804340e-03 -0.0166603559
888 0.4779871776 1.55438155e-03 -0.0113919231
893 0.4810959407 3.40924808e-02 -0.3048749297
898 0.4810959407 3.12804340e-03 -0.0294303584
903 0.4810959407 2.87003329e-04 -0.0023387348
908 0.4816699474 5.77566602e-04 -0.0049301061
913 0.4828250806 6.99451768e-04 -0.0063693897
918 0.4842239841 6.99451768e-04 -0.0068016585
923 0.4856228876 5.77566602e-04 -0.0059358354
928 0.4867780209 2.87003329e-04 -0.0030546338
933 0.4873520275 6.29488655e-03 -0.0804855249
938 0.4873520275 5.77566602e-04 -0.0063525370
943 0.4885071607 1.16229725e-03 -0.0135716425
948 0.4908317552 1.40757942e-03 -0.0176845969
953 0.4936469141 1.40757942e-03 -0.0187633447
958 0.4964620729 1.16229725e-03 -0.0160392818
963 0.4987866674 5.77566602e-04 -0.0080741220
968 0.4999418006 7.62331047e-03 -0.0989066645
973 0.4999418006 6.99451768e-04 -0.0098129830
978 0.5013407042 1.40757942e-03 -0.0196546525
983 0.5041558630 1.70462404e-03 -0.0231366201
988 0.5075651111 1.70462404e-03 -0.0218177622
993 0.5109743592 1.40757942e-03 -0.0166927096
998 0.5137895180 6.99451768e-04 -0.0077919372
1003 0.5151884215 7.62331047e-03 -0.0623509944
1008 0.5151884215 6.99451768e-04 -0.0074411458
1013 0.5165873251 1.40757942e-03 -0.0138886520
1018 0.5194024839 1.70462404e-03 -0.0148824803
1023 0.5228117320 1.70462404e-03 -0.0128450487
1028 0.5262209801 1.40757942e-03 -0.0091785038
1033 0.5290361389 6.99451768e-04 -0.0041151638
1038 0.5304350425 6.29488655e-03 -0.0261579473
1043 0.5304350425 5.77566602e-04 -0.0031880317
1048 0.5315901757 1.16229725e-03 -0.0058729354
1053 0.5339147702 1.40757942e-03 -0.0062176712
1058 0.5367299290 1.40757942e-03 -0.0053398445
1063 0.5395450879 1.16229725e-03 -0.0038206601
1068 0.5418696824 5.77566602e-04 -0.0017188044
1073 0.5430248156 3.12804340e-03 -0.0075308971
1078 0.5492809024 4.12870929e-02 -0.0290556743
1083 0.5492809024 3.78816136e-03 -0.0059828993
1088 0.5568572251 7.62331047e-03 -0.0058929599
1093 0.5721038460 9.23207464e-03 -0.0029900391
1098 0.5721038460 8.47058630e-04 -0.0003648915
1103 0.5737979633 1.70462404e-03 -0.0006403384
1108 0.5772072114 2.06435465e-03 -0.0006590780
1113 0.5813359207 2.06435465e-03 -0.0005946007
1118 0.5854646300 1.70462404e-03 -0.0004836074
1123 0.5888738780 8.47058630e-04 -0.0002475232
1128 0.5905679953 9.23207464e-03 -0.0038475133
1133 0.5905679953 8.47058630e-04 -0.0002565975
1138 0.5922621126 1.70462404e-03 -0.0005557482
1143 0.5956713606 2.06435465e-03 -0.0007696621
1148 0.5998000699 2.06435465e-03 -0.0009078714
1153 0.6039287792 1.70462404e-03 -0.0008753058
1158 0.6073380273 8.47058630e-04 -0.0004823283
1163 0.6090321446 7.62331047e-03 -0.0060327035
1168 0.6242787655 3.78816136e-03 -0.0043095886
1173 0.6318550882 4.12870929e-02 -0.1192421632
1178 0.6318550882 3.78816136e-03 -0.0052951639
1183 0.6394314109 7.62331047e-03 -0.0138845590
1188 0.6546780319 9.23207464e-03 -0.0229820968
1193 0.6731421811 9.23207464e-03 -0.0300431585
1198 0.6916063304 7.62331047e-03 -0.0302116889
1203 0.7068529513 3.78816136e-03 -0.0168254961
1208 0.7144292740 3.40924808e-02 -0.2029184826
1213 0.7144292740 3.12804340e-03 -0.0147927341
1218 0.7206853608 6.29488655e-03 -0.0322029480
1223 0.7332751339 7.62331047e-03 -0.0432564895
1228 0.7485217549 7.62331047e-03 -0.0477528887
1233 0.7637683758 6.29488655e-03 -0.0426682009
1238 0.7763581489 3.12804340e-03 -0.0222452214
1243 0.7826142357 1.69411726e-02 -0.1315577174
1248 0.8164965809 9.17517095e-02 -0.8842490527
1253 0.8164965809 8.41837620e-03 -0.0716141560
1258 0.8333333333 1.69411726e-02 -0.1542894472
1263 0.8672156785 2.05163060e-02 -0.1998973543
1268 0.9082482905 2.05163060e-02 -0.2065471359
1273 0.9492809024 1.69411726e-02 -0.1695718075
1278 0.9831632476 8.41837620e-03 -0.0823291518
I =
-0.566819750152926