If 

$$\int\_0^1xf(x) dx=\int\_0^1f(x) dx = 1$$

prove that

$$\int\_0^1(f(x))^2 dx \geq 4$$

**EDIT**
My attempt is as follows - 
I can use only the $\int xf(x)$dx part to get a bound $\int f^2(x) dx \geq 3$ from cauchy schwarz. I can't think of ways how to incorporate the other given condition.