The Laplace Transform Of $\int _ { 0 } ^ { t } e ^ { \tau } \sin ( t - \tau ) d \tau$

Multiple Choice

The Laplace transform of $\int _ { 0 } ^ { t } e ^ { \tau } \sin ( t - \tau ) d \tau$ is

A) $1 / \left( ( s - 1 ) \left( s ^ { 2 } + 1 \right) \right)$
B) $1 / \left( ( s + 1 ) \left( s ^ { 2 } + 1 \right) \right)$
C) $s / \left( ( s - 1 ) \left( s ^ { 2 } + 1 \right) \right)$
D) $s / \left( ( s + 1 ) \left( s ^ { 2 } + 1 \right) \right)$
E) $1 / \left( ( s - 1 ) \left( s ^ { 2 } - 1 \right) \right)$