I'm not sure where to start with this one either

Find a finite subset of each of the following subspaces for which the subspace is the span of the subset.

{p(x) is an element of P_{2}such that the integral from 0 to 1 of p(x)dx=0}

Hint: A polynomial in P_{2}has the form ax^{2}+ bx + c where a, b, c are elements of R and you will have to integrate.