The function is .

Observe the graph:

The area of shaded region is .

The value of integral is .

(a). Find .

The region bounded between to .

The region is below the -axis.

.

(b). Find .

Apply Additive Interval Property: .

Substitute and .

.

(c). Find .

Apply Additive interval property: .

Substitute and .

.

(d). Find .

Apply constant rule of integration:.

Substitute .

.

.

(e). Find .

Apply sum rule of integration:.

Substitute .

.

.

(f). Find the average value of over the interval .

Average value of the function  on is defined as .

Substitute and .

Substitute .

.

Average value is .

(a). .

(b). .

(c). .

(d). .

(e). .

(f). Average value is .