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?