Find the Volume of the Solid Bounded by the Given $\Omega$

Multiple Choice

Find the volume of the solid bounded by the given function over the specified region $\Omega$ . $f ( x , y ) = x e ^ { y }$ and $\Omega = \left\{ ( x , y ) : 0 \leq x \leq 1 \text { and } x ^ { 2 } \leq y \leq 1 \right\}$

A) $\frac { 3 } { 2 } e$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 2 } e$
D) $e - \frac { 1 } { 2 }$