I am struggling to prove the following problem. Could anyone help demonstrate how this can be done:

Find k so that $\displaystyle f(x) = kx(1-x)$ when $\displaystyle 0<x<1$, or $\displaystyle f(x) = 0$ otherwise.

I understand that the integral of a probability distribution function needs to equal 1, but I cannot demonstrate that it does myself...

Thanks for any help on this