Surface Integrals, Stokes & Divergence · Hard problem

Let $\mathbf F = \nabla f$ with $f(x, y, z) = 3 x^{2} y + 2 y z + 2 z^{2}$. Find $\int_C \mathbf F \cdot d\mathbf r$ along ANY path $C$ from $(2, 2, -2)$ to $(3, 1, 0)$.