On a comparison of Darboux and Riemann integrals in constructive analysis

TL;DR

This paper constructs a specific real-valued function in constructive analysis that is integrable by Riemann but not by Darboux, highlighting differences between these integral concepts.

Contribution

It provides the first known example of a function that is Riemann integrable but not Darboux integrable within constructive analysis.

Findings

Existence of a function integrable by Riemann but not Darboux

Clarification of differences between Riemann and Darboux integrals in constructive context

Advancement in constructive analysis of integrability concepts

Abstract

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