probability density example

Suppose  \(X\) takes values in\( (0,1) \) and has a density

\[f(x)=\begin{cases}c x^2 (1-x)^2 \qquad &x\in(0,1)\\  0 & x \not \in (0,1)\end{cases}\]

for some \(c>0\).

1. Find \( c \).
2. Find \(\mathbf{E}(X)\).
3. Find \(\mathrm{Var}(X) \).