Using \raisebox and \displaylimits on an integral sign

Question

As part of a larger project, I am trying to lower the superscript a of the following integral so that it touches the integral sign itself. Here is the code I am using:

$$\int\displaylimits^{\mathrel{\raisebox{-2pt}{a}}}$$

If I make the /raisebox parameter positive, I can lift a high above the integral sign, but I'm not able to lower it at all.

Answer 1

Interestingly, it appears you need something else in the superscriot and subscript to move the box relative to. Also, there is a limit how far it will move depending on the height and depth.

\documentclass{standalone}
\usepackage{amsmath}

\begin{document}

$\displaystyle x 
\int\displaylimits^{\null\raisebox{-2pt}[0pt][0pt]{$\scriptstyle a$}}_{\null\raisebox{1.2pt}[0pt][0pt]{$\scriptstyle b$}}
\int\displaylimits^a_b$

\end{document}

Answer 2

The result looks hideous. Don’t do it.

\documentclass{article}
\newcommand*\moveintsubscript[1]{%
  \raisebox{-0.3\fontdimen6\scriptfont2\relax}{%
    $\scriptstyle\mkern-12mu#1$}%
}
\begin{document}
Why would you ever want this ugly thing:
\[
\int_{\moveintsubscript{a}}
\]
when you can use
\[
\int\limits_a
\]
just fine?
\end{document}