If $\displaystyle X$ has the uniform distribution $\displaystyle U(-1,3)$, find the probability density function of $\displaystyle Y=X^2$.

Since $\displaystyle -1<x<3, 0<y<9$. Also, $\displaystyle X=\sqrt{Y},-\sqrt{Y}$. I've done some work and ended up with $\displaystyle f(x)=\frac{1}{2\sqrt{y}}$. But when I integrate this from 0 to 9, it does not give me 1. Can I get some help?