Problem 931 (difficulty: 3/10)

If \(\displaystyle f\) is bounded and concave down on \(\displaystyle [a,b]\), then

\(\displaystyle (b-a){f(a)+f(b) \over 2} \ \leq\ \int_a^b f \ \leq\ (b-a)f\Big({a+b \over 2}\Big)\)

Give me another random problem!