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.