Consider two antiderivatives below.
f(x)=-1/x+2 for x>0
f(x)=-1/x for x<0
f'(x)=1/x^2 for all non-zero real values of x
f(1)=1, f(-1)=1
f(x)=-1/x+2 for x>0
f(x)=-1/x+2 for x<0
f'(x)=1/x^2 for all non-zero real values of x
f(1)=1, f(-1)=3
Both satisfy the requirement. Therefore, f(-1) cannot be uniquely determined.
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