Making integrals look prettier with negative spacing for publication

How should I write definite integrals for publication?

Examples:

or

or

I am not sure about how to write the limits correctly.

How should I write definite integrals for publication?

• Don't do anything else the default one: \int_{lower}^{upper}f(x)dx. – Sigur Nov 3 '13 at 15:51
• Use can try and see if you like the result of \usepackage[intlimits]{amsmath} better. – Aditya Nov 3 '13 at 16:18
• I'd do nothing of this kind; perhaps, in some special cases, I'd add a \!. The last three examples are surely wrong. – egreg Nov 3 '13 at 16:27
• Why not use \limits, that's what it's there for, isn't it? This makes the equations quite high, but except in inline mode it's ok IMO. Then there's not much of a gap. Plain underscore is good for the mathematically equivalent \int_{\mathbb{R}}, which I quite like both conceptually (focus on the domain rather than just the boundaries) and visually (one symbol rather than four). Of course that's not much good if you integrate just over e.g. [1,2]. – leftaroundabout Nov 3 '13 at 20:16
• @leftaroundabout Not possible in my case where the direction is very important and there are many of those things and they change direction often. – Léo Léopold Hertz 준영 Nov 3 '13 at 23:03

Let's look at some examples:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\diff}{\mathop{}\!d}

\begin{document}
\begin{gather*}
\int_{-\infty}^{+\infty}               e^{-i2\pi xt}f(x)\diff x   \\
\int_{-\infty}^{+\infty}  \!           e^{-i2\pi xt}f(x)\diff x   \\
\int_{-\infty}^{+\infty}  \! \!        e^{-i2\pi xt}f(x)\diff x   \\
\int_{-\infty}^{+\infty}  \! \! \!     e^{-i2\pi xt}f(x)\diff x   \\
\int_{-\infty}^{+\infty}  \! \! \! \!  e^{-i2\pi xt}f(x)\diff x
\end{gather*}
\end{document}


The first and the second lines seem right; perhaps, due to the low ‘e’ a negative shift is good, so the second line could be preferred.

In no case should the integrand go below the integration bounds. So, starting from the third line the result are on the worse side.