Integration of linear transform of function

Statement

Suppose $F$ is an antiderivative for $f$. Then:

$\int f(mx+\phi )dx=\frac{1}{m}F(mx+\phi )$

where $m$ is a nonzero real number and $\phi$ is a (possibly zero and possibly nonzero) real number).

This is a special case of integration by u-substitution where we put in $u=mx+\phi$.