Let V be a volume in $\mathbb{R}^3$ bounded by a simple closed piecewise-smooth surface S with outward pointing normal vector n. For which one of the following vector fields is the surface integral $\iint\limits_{S}\mathbf{f}\cdot \mathbf{n}dS$ equal to the volume of V ?
A: $\mathbf{f}(\mathbf{r})=(1,1,1)$
B: $\mathbf{f}(\mathbf{r})=\frac{1}{2}(x,y,z)$
C: $\mathbf{f}(\mathbf{r})=(2x,-y^2, 2yz-z)$
D: $\mathbf{f}(\mathbf{r})=(z^2,y^2,1-2yz)$
What I have tried:
So for A and D I have worked out that the curl is $0$ so that rules those 2 out. I don't know how to tackle the other 2.
hint
For that, you need $$\iint_S\vec{f}\cdot \vec{n}ds=\iiint_Vdxdydz$$
or simply that $$\nabla \cdot \vec{f}=1$$
For example, in the case $ C,$ $$\nabla \cdot (2x,-y^2,2yz-z)=$$ $$2-2y+2y-1=1$$