I have a function namely cos(x)/x^2 which I need to integrate in the limits of x = -1 to x = +1. If we plot the integrand (attched xls file, integrand plotted for different number of sampling points), you can see that the integrand is positive all the time inside the limits of integration. Also note that the integrand is singular in the given limit at x=0. Now since this integral is not a simple one to handle, I resorted to Mathematica for solving it. Strangely, Mathematica returns a value of negative 2.97 for the integral (I only remember the first two digits after decimal point). Question is, when the integrand is positive all the time, how can the integral be negative. When I try some online integration tools for this function, they return with message that this integral is likely to be a nonelementary kind. I know funny things do happen at the singularities but the answer from Mathematica does not make sense to me. Does anyone have any comments on this? Thanks for your help. gcd. PS. I tried to evaluate the integral with Trapezoid rule (see yellow box in attached xls file) and the answer returned does make sense.