However, because f(x) is a very continuous function, the equal sign cannot be established (otherwise, continuity can be used to prove that every point is m).
In addition, if f(x) is nonnegative in [a, b], there is ∫{a, b} f(t)dt ≥ 0.
F(x) is still a very continuous function, and the equal sign cannot be established.
So 0
Let f(x) get the maximum value m on [a, b] at x = e, and f(a) = f(b) = 0.
F(x) is continuous. According to the intermediate value theorem, there are c and d on (a, e) and (e, b) respectively, so that f (c) = (1(b-a)) ∫ {a, b} f (t) dt = f (d).