Absolute Integrable Sinc function
The question has an answer on Math SE. The argument goes as follows:

\begin{eqnarray}
\int_{-\infty}^\infty \left| \frac{\sin t}{\pi t} \right|dt &amp;=&amp; \frac{1}{\pi}\sum_{n=-\infty}^\infty \int_{n\pi}^{(n+1)\pi} \left| \frac{\sin t}{t} \right| dt \\
&amp;&gt;&amp; \frac{1}{\pi} \sum_{n=-\infty}^\infty \frac{1}{|n+1|\pi}\int_{n\pi}^{(n+1)\pi} |\sin t|dt \\
&amp;=&amp; \frac{2}{\pi^2} \sum_{n=-\infty}^\infty \frac{1}{|n|}\\
&amp;\rightarrow&amp; \infty
\end{eqnarray}
where in each interval $[n\pi, (n+1)\pi]$ we lower bound $1/t$ with $1/(n+1) \pi$.