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 $(0, 0, -1)$ to $(3, -2, -1)$.