Question about a substitution in an integral So studying integrals for a short duration I found this example of an equation. It goes the following way:
$\int_{-r}^r \! \sqrt{r^2-y^2} \, \mathrm{d}y. \stackrel{y=rz}{=} \int_{-1}^1 \! r^2 \sqrt{1-z^2} \, \mathrm{d}z. $
If I get this right $y$ has been substituted with $rz$. Why could this substitution be made and why could $r^2$ be extrated from the root and not just $r$ ? I think I am missing something bigger here, but I just don't get it.
If you need further context for this equation, message me.

$r$ is extracted and then multiplied by $dy=rdz $
