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!