E of symmetry when the domain of integration is symmetric about the origin with respect to at least one of the ables of integration and the integrand is odd wit

Use of Symmetry When the domain of integration is symmetric about the origin with respect to at least one of the ables of integration and the integrand is odd with respect to this variable, the integral is equal to zero, the integrals over the two halves of the domain have the same absolute value but opposite signs. en the integrand is even with respect to this variable, the integral is equal to twice the integral over dll or the domain, as the integrals over the two halves of the domain are equal. Can anyone explain this.