SEEMOUS 2008 Problem 4

Let $n$ be a positive integer and $f:[0,1]\to\mathbb R$ be a continuous function such that $$\int^1_0x^kf(x)dx=1$$ for every $k\in\{0,1,\ldots,n-1\}$ . Prove that $$\int^1_0f(x)^2dx\ge n^2.$$