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

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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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     author = {A. A. Vladimirov},
     title = {On a~comparison of {Darboux} and {Riemann} integrals in constructive analysis},
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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/