Answer
See below.
Work Step by Step
Use formula:$ \int_a^b c dx =c (b-a)$
Consider LHS
Then, we have
$ av(f) (b-a)=\int_a^b f(x) dx$
This can be re-arranged as:
$ av(f)=\dfrac{1}{(b-a)} \int_a^b f(x) dx$
Thus, the result has been verified by the definition.