Answer: 34.5
Explanation
Your teacher wants to know the area under the curve from x = -5 to x = 5.
The region from x = -5 to x = -2 is a trapezoid which I'll denote as portion A.
Portion B goes from x = -2 to x = 0 which is a right triangle.
Portion C goes from x = 0 to x = 5 which is a larger right triangle.
The next section will show the scratch work to find each sub-area.
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Area of trapezoid = 0.5*height*(base1+base2)
A = 0.5*3*(3+6)
A = 13.5
Area of triangle = 0.5*base*height
B = 0.5*2*6
B = 6
C = 0.5*base*height
C = 0.5*5*6
C = 15
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The areas of portions A, B, and C are 13.5, 6, and 15 in that exact order.
Add up those sub-areas to get the final answer.
13.5+6+15 = 34.5
