Let the functions $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by
$$f(x) = e^{x - 1} - e^{-|x - 1|}$$ and $$g(x) = \frac{1}{2}(e^{x - 1} + e^{1 - x})$$.
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

$$\left(2 - \sqrt{3}\right) + \frac{1}{2}\left(e - e^{-1}\right)$$

B

$$\left(2 + \sqrt{3}\right) + \frac{1}{2}\left(e - e^{-1}\right)$$

C

$$\left(2 - \sqrt{3}\right) + \frac{1}{2}\left(e + e^{-1}\right)$$

D

$$\left(2 + \sqrt{3}\right) + \frac{1}{2}\left(e + e^{-1}\right)$$