Integration with a fraction

Can someone please help me with this problem. Please see the attached image.

The integration when removing the min and max is also provided, how is the answer x2/2 - x3/6? Do we not do anything with the 1 - 1/2 part? and the +2 part? Are we only looking at (x2-2x)/2?

I appreciate the help.

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Answers and Replies

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mathman
Science Advisor
The integrand is x - x2/2.

HallsofIvy
Science Advisor
Homework Helper
$$-\frac{1}{2}\left(x^2- 2x+ 2\right)= -\frac{1}{2}x^2+ x- 1$$
Adding 1 to that gives the integrand
$$-\frac{1}{2}x^2+ x$$
as mathman says.

Thanks, that is exactly what I needed to know.