Using...tensor
package.....with the enviroment mathtools
...an alternative a bit more complicated :-)
\documentclass[12pt]{article}
\usepackage{mathtools}
\usepackage{tensor}
\begin{document}
\[\lim_{\Delta\phantom{\to}0} \Delta \tensor*[^T_t]{\bigg\lvert \frac{df(t)}{dt}\bigg\rvert}{^2} dt\]
\end{document}

Update 1
Using \lower-0.01em
with \hbox
and \scriptstyle
it is possible a nice alignment between T
and 2
.
\documentclass[a4paper,12pt]{article}
\usepackage{mathtools}
\usepackage{tensor}
\begin{document}
\[\lim_{\Delta\to 0} \Delta \tensor*[^{\lower-0.01em \hbox{$\scriptstyle T$}}_t]{\bigg\lvert \frac{df(t)}{dt}\bigg\rvert}{^2} dt\]
\end{document}

\lim\limits_{\Delta\to 0}\; \Delta_{t=0}^{t=T}\;\left| \dfrac{d\,f(t)}{dt} \right|^2\; dt