If $\frac{d}{dx}\{f(x)\} = g(x)$, then $\int_a^b f(x) g(x) dx$ is equal to
- A$\frac{1}{2}\left[f^2(b) - f^2(a)\right]$
- B$\frac{1}{2}\left[g^2(b) - g^2(a)\right]$
- C$f(b) - f(a)$
- D$\frac{1}{2}\left[f(b^2) - f(a^2)\right]$
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