1. The problem statement, all variables and given/known data Evaluate ∫(1/x)sin^2(x)dx from -a to a 3. The attempt at a solution Mathematica doesn't want to evaluate this because of the lack of convergence. I think it is zero. When we consider non-zero values of x in the associated riemann sum, the integrand is odd and so contributions from x and -x cancel out. I can make the Δx in the riemann sum arbitrarily small, so when we consider the step near zero, sin^2 x is almost exactly equal to x^2 and that term in the sum gets replaced to xΔx where x is very nearly zero as is delta x. In other words, the integral is zero. Is this kind of reasoning valid?