Let

*F*(*x*) be an indefinite integral or antiderivative of

* f*(*x*). Then

where

*x = g *(*u*) is a substitution. Accordingly, the inverse function

*u = g*^{ −1}(*x*) describes the dependence of the new variable on the old variable.

It's important to remember that the differential

*dx* also needs to be substituted. It must be replaced with
the differential of

the new variable *du*.
For definite integrals, it is also necessary to change the limits of integration.
See about this on the page "

The Definite Integral and Fundamental Theorem of
Calculus".