Suppose
f(x) =
\left\lbrace
\begin{array}{rll}
1 && \mbox{ if } 5 \leq x \lt 8,
\\
-4 && \mbox{ if } 8 \leq x \leq 11.
\end{array}
\right.

(a) Evaluate the definite integral by interpreting it in terms of signed area.

**Suggestion:** Draw a picture of the region whose signed area is represented by the integral. Then find the signed area using formulas from high school geometry.

(b) Find the average value of

Average value =

You can earn partial credit on this problem.