The Surface Integral $\int \int$ S $x y z d S ,$

Multiple Choice

The surface integral $\int \int$ S $x y z d S ,$ where S is $x ^ { 2 } + z ^ { 2 } = 4$ between $y = 1$ and $y = 3 \text {, }$ is

A) $\frac { 32 \pi } { 3 }$
B) $\frac { 15 \pi } { \sqrt { 2 } }$
C) 0
D) $\frac { \sqrt { 3 } } { 6 }$
E) $\frac { 32 \pi } { 7 }$