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Calculate the area bounded by the x-axis and the function f(x)= -(x-a)(x-b), where a<b and a and b are constants. Please do it out in steps so I can understand it, and try to simplify the final answer and leave it in factored form.

Frankly, I would multiply out the polynomial, then integrate

f(x)= -(x-a)(x-b)
= -x^2 + ax + bx -ab

Now integrate it.
I will be happy to critique your work.

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