Surface Integrals, Stokes & Divergence · Hard problem

Let $\mathbf F = \nabla f$ with $f(x, y, z) = x^{2} y + 2 y z + 3 z^{2}$. Find $\int_C \mathbf F \cdot d\mathbf r$ along ANY path $C$ from $(3, 2, 2)$ to $(-2, 1, -2)$.