Solution
= Solution
The <parallel axis theorem> says that for an axis through a body's <centre of mass> and a parallel axis at perpendicular distance $d$,
$$
\boxed{I=I_{\rm cm}+Md^2,}
$$
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>.