Need to know this answer ? integrals?

Question

i have already solved this but i need to know of its correct, plz tell me the answer:
integration of (sinx/ 1+cos^2x)dx
upper limit pi lower limit 0.

Answer 1

Put cos x = z so-sinx*dx =dz So you get the integral between (upper limit -1,lower limit 1) of - dz/(1+z^2) which is-Arctan(z) =-arctan(-1) +arctan(1) = pi/2

Answer 2

check out in "advanced engineering mathematics" by erwin kreyszig, 8e, u'll never get such doubts again. (i believe the 9th e is out).