Show that: $\int_{0}^{1}f\left(x\right)dx\ .\ \int_{0}^{1}g\left(x\right)dx\ \le\ \int_{0}^{1}f\left(x\right)g\left(x\right)dx$
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$