You have to solve a 4x4 system of linear equations.

The polynomial is of the form The first three data give you three of the equations you need in order to determine a, b, c, and d.

Since the integral of the derivative of f between 0 and 2 is equal to f(2)-f(0), you have a fourth equation here. So, have a happy Gauss-elimination (or whatever way you call it) practice!