Let the functions $f : \mathbb { R } \rightarrow \mathbb { R }$ and $g : \mathbb { R } \rightarrow \mathbb { R }$ be defined by $$f ( x ) = e ^ { x - 1 } - e ^ { - | x - 1 | } \quad \text { and } \quad g ( x ) = \frac { 1 } { 2 } \left( e ^ { x - 1 } + e ^ { 1 - x } \right)$$ Then the area of the region in the first quadrant bounded by the curves $y = f ( x ) , y = g ( x )$ and $x = 0$ is (A) $( 2 - \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e - e ^ { - 1 } \right)$ (B) $( 2 + \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e - e ^ { - 1 } \right)$ (C) $( 2 - \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e + e ^ { - 1 } \right)$ (D) $( 2 + \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e + e ^ { - 1 } \right)$
Let the functions $f : \mathbb { R } \rightarrow \mathbb { R }$ and $g : \mathbb { R } \rightarrow \mathbb { R }$ be defined by
$$f ( x ) = e ^ { x - 1 } - e ^ { - | x - 1 | } \quad \text { and } \quad g ( x ) = \frac { 1 } { 2 } \left( e ^ { x - 1 } + e ^ { 1 - x } \right)$$
Then the area of the region in the first quadrant bounded by the curves $y = f ( x ) , y = g ( x )$ and $x = 0$ is\\
(A) $( 2 - \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e - e ^ { - 1 } \right)$\\
(B) $( 2 + \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e - e ^ { - 1 } \right)$\\
(C) $( 2 - \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e + e ^ { - 1 } \right)$\\
(D) $( 2 + \sqrt { 3 } ) + \frac { 1 } { 2 } \left( e + e ^ { - 1 } \right)$