I have an example of an equation where I don't know how the right hand side is derived from left hand side. It looks very weird as the differential changes. Notice that $m$ and $c$ are constants.

$$\frac{m}{2} \int \frac{\textrm{d}v^2}{\sqrt{1-\frac{v^2}{c^2}}} = \frac{-mc^2}{2} \int \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \mathrm d\left(1-\frac{v^2}{c^2}\right) $$

Which rules apply here? Could anyone explain this or provide me with links to any good websites? Than you.