Change of variable in Riemann integration revisited

TL;DR

This paper offers a new, clearer proof of a general change of variable theorem in Riemann integration, along with an extensive review of related literature.

Contribution

It provides a novel proof technique for Kestelman's theorem and a comprehensive bibliographical analysis of related results.

Findings

New proof of Kestelman's change of variable theorem

Enhanced clarity in understanding Riemann integration changes

Extensive bibliographical review of related proofs

Abstract

We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related results and proofs.