Assume $\displaystyle f,g \in R([a,b])$,and $\displaystyle m_{1} \leq f(x) \leq M_{1},m_{2} \leq g(x) \leq M_{2}$,Then

$\displaystyle \frac{1}{b-a}\int\limits_a^b{f(x)g(x)}dx - \frac{1}{(b-a)^2}\int\limits_a^b{f(x)}dx\int\limits_a^b{g(x)}d x \leq \frac{(M_{1}-m_{1})(M_{2}-m_{2})}{4}$


thanks very much.....