Geodesic
Comparison of Some Trigonometric Integrals
Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 301-308

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We show that Preiss–Thomson's AS-integral is inconsistent with Burkill's SCP-integral, James' $\mathrm P^2$-integral, and Denjoy's totalization $\mathrm{T}_{2s}$ over the class of functions with continuous primitives.
Keywords: symmetric Cesàro derivative, approximate symmetric derivative, Denjoy's totalization $\mathrm T_{2s}$, Burkill's SCP-integral, Preiss–Thomson's AS-integral, James' $\mathrm P^2$-integral. 
@article{MZM_2018_104_2_a12,
     author = {P. A. Sworovsky and V. A. Skvortsov},
     title = {Comparison of {Some} {Trigonometric} {Integrals}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {301--308},
     publisher = {mathdoc},
     volume = {104},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a12/}
}
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P. A. Sworovsky; V. A. Skvortsov. Comparison of Some Trigonometric Integrals. Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 301-308. http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a12/