Answer
$\frac{3}{2}$
Work Step by Step
av(f)=$(\frac{1}{1-(-2)})\int^{1}_{-2}(t^2-t)dt$
=$\frac{1}{3}\int^{1}_{-2}t^2dt-\frac{1}{3}\int^{1}_{-2}tdt$
=$\frac{1}{3}\int^{1}_{0}t^2dt-\frac{1}{3}\int^{-2}_{0}t^2dt$
=$\frac{1}{3}(\frac{1}{2}-\frac{4}{2})$
=$\frac{1}{3}$($\frac{1^3}{3}$)-$\frac{1}{3}$($\frac{-2^3}{3}$)+$\frac{1}{3}=\frac{3}{2}$
