If $X$ is a random variable with finite mean $\mu$ and variance $\sigma^2$, how do I show that the estimate
\begin{equation*} P[\mu − d\sigma < X < \mu + d\sigma] ≥ 1 − 1/d^2~\forall d>1 \end{equation*}
holds? I found this in a book but unable to see the proof. Note that $X$ may not be normal.