Let $f$ and $g$ be two real-valued continuous functions defined on the closed interval $[a, b]$, such that $f(a) < g(a)$ and $f(b) > g(b)$. Then the area enclosed between the graphs of the two functions and the lines $x = a$ and $x = b$ is always given by\\
(A) $\int_a^b |f(x) - g(x)| \, dx$\\
(B) $\left|\int_a^b (f(x) - g(x)) \, dx\right|$\\
(C) $\left|\int_a^b (|f(x)| - |g(x)|) \, dx\right|$\\
(D) $\int_a^b ||f(x)| - |g(x)|| \, dx$.