Math: overwrite \int command

Question

I wish I could override the \ int command, so that each integral is rendered this way.

Yes, I know the command to display it this way is \int\displaylimits_a^b, but I would like to overwrite the original command. Some idea?

Answer 1

\int is defined as

\DeclareRobustCommand\int{\intop\nolimits}

so you could simply use \intop otherwise \let\int\intop if you want to use \int

Answer 2

Use the relevant option in amsmath:

\documentclass{article}
\usepackage[intlimits]{amsmath}

\begin{document}

\[
\int_{a}^{b} f(x)\,dx
\]

\end{document}