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We approach the Riemann integral via generalized primitives to give a newproof for a general result on change of variable originally proven by Kestelmanand Davies. Our proof is similar to Kestelman's, but we hope readers will findit clearer thanks to the use of a new test for the Riemann integrability (whichwe introduce in this paper) along with some ingredients from some other morerecent proofs available in the literature. We also include a bibliographicalreview of related results and proofs. Although this paper emphasizes in thechange of variable theorem, our contributions to the Riemann integration theoryare of independent interest. For instance, we present a very simple proof tothe fact that continuous functions are integrable which avoids the use ofuniform continuity.

Riemann integration via primitives for a new proof to the change of variable theorem