First use algebra to find where the enclosed area is. Then integrate the difference between the functions from one intersection to the other.
Drawing a graph will help a lot.
It seems to me, after drawing a sketch, that the two curves never intersect, and that the "enclosed area" between them is infinite. Are you sure the second curve is not x^2 -2 ? In that case they would intersect at -2 and +2
find the area enclosed by the curves y=absolute value of x and y=x^2+2
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