Past exam of the mathematics course of the University of Cambridge / 2012 / ia / Paper 4 / 11B / a

The parallel axis theorem says that for an axis through a body's centre of mass and a parallel axis at perpendicular distance $d$,where $M$ is the total mass. The displacement is the distance between the two parallel axes; neither axis may be arbitrary in place of the center-of-mass axis. Expanding the squared distances of mass elements gives this formula, since the cross term integrates to zero at the centre of mass.