If $f$ and $g$ are continuous functions in $[0, a]$ satisfying $f(x) = f(a - x)$ and $g(x) + g(a - x) = 4$,then $\int_{0}^{a} f(x) g(x) dx$ is equal to:
- A$\frac{1}{2} \int_{0}^{a} f(x) dx$
- B$2 \int_{0}^{a} f(x) dx$
- C$\int_{0}^{a} f(x) dx$
- D$4 \int_{0}^{a} f(x) dx$
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