sorry about the last post. How does the book get from
to a negative integral going from pi/2 to 3pi/2 cot(t) + integral going from 3pi/2 to 2pi cos(t)?
so they split the integral into two parts. the interval on which it is negative and the interval on which it is positive. on the interval the function was negative, they took the negative of the function (which is positive) for that interval and integrated it