I'm not sure where to start with this:
Define h: P_{2} --> P_{3 }by h(p(x)) = xp'(x) + the integral from 0 to x of p(t) dt.
a. Verify that the codomain of h is in fact P_{3 }and prove that h is a linear transformation.
b. Find h(p(x)) where p(x) = x^{2} + x + 1.