Consider a calculus formula like d/dx(sinx) = cos(x). The key thing to notice isthat this is only true when x is in radians. To get a similair formula for degrees, you would write:
d/dx(sin(x degrees)) = d/dx(sin(pi\*x/180 radians)) = pi/180 cos(x degrees). You could choose any other angle measure, and you would get a similair constant at the front. The "beautiful" thing about radians is that constant is exactly 1.
During the derivation of your problem, they will have used the fact that the integral of 1/(1+x\^2) is arctan(x), but similairly, this is only true when x is in radians. If you wanted to use arctan(x) in degrees, you woud get a constant of pi/180 in front that would cancel out the 90 degrees, giving pi/2 again.