Sketch and find the area bounded by:
y=-x^2 + 2x + 3 ; y=3
The graph ends up looking like an upside down paraboloid bound at -2 and +2 with a y intercept at (0,7)
integrate: -1/3 x^3 + x^2 + 3x
@ x=+2 that equals 22/3
@ x=-2 that equals 2/3
22/3 + 2/3 = 24/3 that would be all the area under the curve from [-2,2] = 8 <--but that seems wrong if I went from [0,2] it would be the 22/3 so my thinking is wrong there somewhere.
then the other function integrate y=3 = 3x
3x @ 2 = 6
3x @ -2 = -6
6+6=12
subtract the area in the second function from the first function: 22/3 - 36/3 and wrong answer

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Seems like your teacher described everything blow by blow

oh no everything after the second line is me working it....

You wrote a lot, what's your question? (Good work, by the way.)

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