1. The problem statement, all variables and given/known data I need to find the Fourier coefficients for a function f(t)=1 projected onto trigonometric polynomials of infinite order 2. Relevant equations Equation finding the first coefficient, the constant term: 3. The attempt at a solution So I feel quite stupid because this should be a very simple integral. The integral of a monotonic function over an interval that is symmetric about the origin SHOULD be equal to zero. It seems my book has just integrated from 0 to pi for first Fourier coefficient. I'm here pulling my hair out trying to figure out why/how this is correct because the two integrals certainly are not equivalent. Can someone help me out here?