Remember that -csc^2(x) is a known derivative; it is the derivative of cot(x).
Keeping that in mind, let's put a negative there, and then offset it with another negative, which can conveniently be placed outside of the integral.
(-1) Integral ( -csc^2(x) dx )
Which evaluates to
(-1) cot(x) + C
-cot(x) + C