Geodesic
On a comparison of Darboux and Riemann integrals in constructive analysis
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XII, Tome 407 (2012), pp. 7-16 
A. A. Vladimirov. On a comparison of Darboux and Riemann integrals in constructive analysis. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XII, Tome 407 (2012), pp. 7-16. http://geodesic.mathdoc.fr/item/ZNSL_2012_407_a0/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An example of constructive (in A. A. Markov's sense) real-valued function of one real variable which is integrable by Riemann, but is not integrable by Darboux, is constructed.

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