Let [0,1] --->R be continuous. (little f above arrow)

Define [0,1] --->R (capital F above arrow) by F(x) = $\displaystyle \displaystyle\int^{x^2}_0 f \, $

Show that F is differentiable with $\displaystyle F'(x) = 2x f(x^2). $

I seriously have worked on this question for hours and have got nowhere! Can anyone give me any help at all?!

Thanks in advance!