Surface Integrals, Stokes & Divergence · Hard problem

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