How do we find integral closure? 
Find the integral closure of $\mathbb C[x^2,x^2-1] $ in $\mathbb C(x)$

I don't know much about integral closure,I've just learned about it.How do we find integral closure in practice ? Thanks for your help.

$\mathbb C[x^2]\subset\mathbb C[x]$ is integral ($x$ is a root of $T^2-x^2\in\mathbb C[x^2][T]$), so the integral closure of $\mathbb C[x^2]$ in $\mathbb C(x)$ is $\mathbb C[x]$ since the last one is integrally closed.
