You should use the principal branch which means answers lie in the range [-pi/2,pi/2] if you include -infinity and +infinity.
The question asks for the area bounded by y=4 and 4/(1+x^2) from x=-1 to x=1.
I used definition integral to do this question and get (4x - 4*arctan(x)) from x=-1 to x=1.
However, when I plug in the numbers, I don't know which value to use for arctan(-1). If I use arctan(-1) = 3 pi/4, I would get an answer from the answer key. (The answer key says arctan(-1) = -pi/4.
How do I know which value I should use?
Please help me! Thanks!