Don't really know how to prove this at all, I'm much appreciative of any help.

Let f : [a,b] ⇒ ℝ be a continuous function. Show that there exists a w in [a,b] such that

a

∫ f(t)dt = f(w)(b-a)

b

Here is the hint that ineedto use to solve this problem:

f attains a smallest value A and a largest value B. Show that:

-----------a

A ≤ 1/(b-a)∫ f(t)dt ≤ B

-----------b

Thank you again for the help!