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

\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.....