Let $\displaystyle a + b =4$, $\displaystyle a < 2$ and $\displaystyle g(x)$ be monotonically increasing function of x. Prove that $\displaystyle f(x) = \int_{0}^{a} g(x)\ dx + \int_{0}^{b} g(x)\ dx$ increases with increase in $\displaystyle (b - a)$.