Integration of linear transform of function

Statement

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

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

where $m$ is a nonzero real number and $\varphi$ is a (possibly zero and possibly nonzero) real number). The "+ C" is the usual arbitrary constant addition.

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