I could use some help with the following...

On $\displaystyle P_{2}(R)$, consider the inner product given by $\displaystyle <p,q>=\int_0^1 p(x)q(x) dx$. Apply the Gram-Schmidt procedure to the basis $\displaystyle (1,x,x^2)$ to produce an orthonormal basis of $\displaystyle P_{2}(R)$.