Prove $(\int_0^1f(x))^2>\int_0^1f^3(x)$

Question

Possible Duplicate:
Prove that $\int_0^x f^3 \le \left(\int_0^x f\right)^2$

Assume $f(x)$ is derivable in[0,1],and when $x\in$(0,1), $0<f^{'}(x)<1,f(0)=0$

Prove

$(\int_0^1f(x))^2>\int_0^1f^3(x)$