Employing a variation of my answer at Integral Sign $\int...$, I define a new operator \uint
and show the comparison to \int
in the MWE below.
This approach takes a traditional \scriptstyle
integral sign, rotates it 8 degrees, and scales it up to the same vertical extent as a normal integral sign when employed in the current mathstyle.
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator*{\uint}{\scalerel*{\rotatebox{8}{$\!\scriptstyle\int\!$}}{\int}}
\usepackage{scalerel}
\usepackage{graphicx}
\parskip 1ex
\begin{document}
\[
f=\int_0^t A d\tau =\uint_0^t A d\tau
\]
\centering
\(
f=\int_0^t A d\tau =\uint_0^t A d\tau
\)\par
\(
\scriptstyle f=\int A d\tau =\uint A d\tau
\)\par
\(
\scriptscriptstyle f=\int A d\tau =\uint A d\tau
\)
\end{document}

If the integral sign is perceived as just a bit too bold, then the we can scale a \textstyle
integral sign instead:
\DeclareMathOperator*{\uint}{\scalerel*{\rotatebox{8}{$\!\textstyle\int\!$}}{\int}}

\[\int_{min}^{max} f(x) dx\]
for example.