change of variables (fundamental theorem of calculus)

Question

$\int_{0}^{\sqrt \pi}x\cos(x^2)dx = \int_{0}^{\pi}\frac{\cos(s)}{2}ds$.

Could you tell me how to transform the integral from left to right, using the fundamental theorem of calculus?

Let $s(x)=x^2$. Then, how can I eliminate $x$ in the first equation?

Thank you in advance.

Answer 1

You get it from this: $ds=2x dx$