Question

what is average value of cos(x) on the interval [-3,5]?

Answer 1

Well you know that cos(x) is sketched between 1 and -1 on the graph. And you are looking at the average value between two points.

Answer 2

the average value of f(x) on the interval [a,b] is

∫[a,b] f(x) dx
-----------------------
(b-a)

so just plug in your values.