# Integration of Composite Functions.

1. Feb 7, 2012

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We were discussing integration recently and when u-substitution came up I got to thinking about under what conditions some composition $f \circ g$ of real functions was Riemann integrable. I looked around and the only combination that is for sure integrable for which I could find a proof is if $f$ is continuous and $g$ is Riemann integrable. But again thinking about u-sub I thought what if $g$ were not only continuous but differentiable (and $f$ Riemann integrable) and/or continuously differentiable as that is much stronger condition. After some Googling I found a paper which contains exactly that as a proposition, but there was no proof given. What would the proof be, or how would one go about proving it?