This would be a case of

Differentiation under the integral sign - Wikipedia, the free encyclopedia

e.g. page 8 here:

http://www.math.uconn.edu/~kconrad/b...ffunderint.pdf

Just in case a picture helps...

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!