im still stuck. i need help.

Question

evaluate the integral
∫sinx /(1+x^2) dx from -1 to 1

Answer 1

The integrand is an odd function of x, therefore the integral will be zero.

As an exercise try to prove that if
f(-x) = -f(x) that the integral from
-r to r of f(x) dx is zero, e.g. by splitting it from -r to zero and from zero to r and then by substituting
x =-t in the first integral, that inttegral then becomes minus the second integral, so they cancel.