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**toffeefan** Determine the area bound by y=-x^2 + x + 1 and y = |x|?

I'm not sure if my approach is right, can someone please help?

Firstly i let y=x and y=-x and sub it in y=-x^2 + x + 1 to find the possible intersection points.

For the substitution of y=x to the curve equation, there are 2 answers for x, one is negative while the other is positive. I choose the positive solution while neglecting the negative solution.

For the substitution of y=-x to the curve equation, there are also 2 answers for x, one is negative while the other is positive. I choose the negative solution while neglecting the positive solution.

So for integration to determine the areas, i split into 2 parts. one part is the integration of the negative solution to 0 using y=-x^2 + x + 1 minus y=-x.

The other part is the integration from 0 to the positive solution using y=-x^2 + x + 1 minus y=x.

Finally, adding the 2 integrals give me the answer. May i know is this approach correct? Thanks.