[brianpan]

An integral can be used to find the area under a curve by summing infinitesimally small areas.

The point isn't to walk to the end of the infinity. It's to use it as a tool to calculate something in a different or previously impossible way.

All tools are arbitrary without an application. But sometimes you have to figure out what's possible before you can try to find an application.

[Kranar]

That's one interpretation but it's kind of shaky without a theory of infinitesimals, and when you do work with a theory of infinitesimals it turns out not to be all that much better than working with the more traditional delta/epsilon approach, which is really quite rigorous and can be explained without the use of any infinities.