Properties of the Average Value of a Function

I. The average value of a function $$f(x)$$ on the interval [$$a, b$$] is given by $$\frac{1}{b-a}\int_a^b f(x)\,dx$$.

II. Dividing $$\int_a^b f(x)\,dx$$ by $$b$$ yields the average value of the function on [$$a, b$$].

III. If $$f(x)$$ is constant over [$$a, b$$], then its average value is that constant.

Which of the above statements are true regarding the average value of a function on an interval?