Question

How does the answer is pi/2 and not 0 for the question lim as t1-->-∞ from t1 to 0 integral (1/(1+x^2))dx

Answer 1

remember that the principal values for arctan(x) lie in (-π/2,π/2)

so, the integral is
arctan(0) - arctan(t1)
and the limit as t1 -> -∞ arctan(t1) is -π/2