$\text { Find the area of the shaded region for the function } y = \frac { e ^ { x } } { 1 + e ^ { 2 x } } \text {. }$

Multiple Choice

$\text { Find the area of the shaded region for the function } y = \frac { e ^ { x } } { 1 + e ^ { 2 x } } \text {. }$

A) $\frac { \pi } { 12 }$
B) $\frac { \pi } { 4 }$
C) $\frac { \pi } { 3 }$
D) $\frac { 5 \pi } { 12 }$
E) $\frac { \pi } { 6 }$