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Is it possible without creating a new font to define a new math symbol (e.g. with \newcommand) and then use it with such commands as \limits, _ and ^ (up and down limits)?

For example, I define it like this:

\usepackage{graphicx}
\newcommand{\bigrint}{\scalebox{1.2}[1] {\rotatebox[origin=c]{15}{$\displaystyle\int$}}}
\newcommand{\rint}[2]{ \substack{\hspace{-4pt} #2 \\ \hspace{-5pt} \bigrint \hspace{-3pt}\\ #1}\hspace{-1pt} }

And I want to use it like \rint_1^2.

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2 Answers 2

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\documentclass[a4paper]{article}
\usepackage{graphicx,amsmath}
\newcommand{\bigrint}{%
  \hbox to .2em{\hss\scalebox{1.2}[1] {\rotatebox[origin=c]{15}{$\displaystyle\int$}}\hss}}
\newcommand{\rint}{\mathop{\bigrint}\displaylimits}

\begin{document}
\[\rint_a^b\]
\end{document}
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Here is an alternative way which works I believe the same as you want:

\DeclareMathOperator{\di}{d\!}

\[
    \int\limits_a^b\! x\di x = \tfrac{1}{2}x^2\Big|_a^b
\]

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