Not quite. According to your pdf, Pr(Y > 1) = 0 ...... Is that correct ....?

If -1 < x < 2 it's clear that 0 < x^2 < 4 => 0 < y < 4. Therefore f(y) = 0 for y > 4 or y < 0.

So you have to find the pdf for Y when . For such values of y, the cumulative density function is given by .