The question is done correctly.
When you differentiate
-x^-1 you get x^-2
and all the arithmetic was done correctly.
If this an "area between curves" type, I have seen this before.
The function f(x) = 1/x^2 is discontinuous at x=0
so even though calculation-wise we come up with the answer above, it would be meaningless.
The answer is wrong because function x^(-2)>0 on [-2,2] except x=0 =>integral>0
This is Improper integral which is divergent.
x^(-1)-->infinity if x-->0
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