2 answers
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A quick sketch will show a downwards opening parabola with
x - intercepts of -2 and 6
So you simply need
∫ (−x^2+3x+10) dx from -2 to 6
= [ -(1/3)x^3 + (3/2)x^2 + 10x] from -2 to 6
= ...
you do the arithmetic