Is this the correct first step:
Let ax^2 + bx + c be and element of W.
Then the integral from 0 to 1 of ax^2 + bx + c = 0
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.