Answer
$0$
Work Step by Step
Stoke's Theorem: Let us consider that $C$ be the closed curve which encloses surface $S$ for a vector field $F$. This also states that the line integral and the surface integral must be equal. That is,
$\oint_C F \ dx=\iint_S (\nabla \times F) \cdot n \ dS$
Here, $\nabla \times F=\begin{vmatrix} i&j&k \\ \dfrac{\partial}{\partial x} & \dfrac{\partial}{\partial y} & \dfrac{\partial}{\partial z} \\ y & xz & -y \end{vmatrix}=(-1-x,0,z-1)$ and $n=(-z_x, -z_y,1) =(0,0,1)$
Thus, the surface integral can be computed as:
$\iint_S (\nabla \times F) \cdot n \ dS=\iint_S (-1-x,0,z-1) \cdot (0,0,1) \ dS\\=0$
