What is the average rate of change of f over the interval -1 is less than or equal to x less than or equal to 1?

Without an illustration of f(x), or a function f(x), the rest of us can help you only in the most fundamental way.

Average rate of change of f(x) on the interval [-1,1] is as follows:
              f(1) - f(-1)         f(1)-f(-1)
ARC =   =
                1 - (-1)                 2