Surface Integrals, Stokes & Divergence · Hard problem

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