Surface Integrals, Stokes & Divergence · Hard problem

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