Arch Linux packager here. This is holding back the package version from getting bumped in our official repos too.
A bit of a test drive suggests that this issue with integrals is not present when using Libertinus Math.
I don't have anything handy to test math mode, but you might review if this issue has been addressed in the Libertinus fonts fork. There is a new OpetType math companion font as well with many glyph issues sorted out for use in math typesetting. If you check it out and there is a problem still please feel free to open a bug report against Libertinus on the GitHub issue tracker and I'll take a look.
Just for the record, I just checked specifically and this issue has been addressed in the Libertinus fonts fork. The stylistic alternate set (+salt) has a less snazy italic J shape that would be suitable where the other one is not.
Just for the record, this issue has been addressed in the Libertinus fonts fork.
Given that this project has been unmaintained for years I would not expect this to get fixed. I did just check this in the Libertinus fonts fork and confirmed the issue. I agree the old style glyph shape should not change based on the horizontal alignment feature +tnum vs. +pnum. I've opened a corresponding issue report and plan to fix this there eventually.
Just for the record, I checked this issue against the Libertinus fonts fork. The situation has improved (all letters have +sups lookps), but there is still a weight issue in that not all of them are bold! I've opened a corresponding issue there. Given that this project is unmaintained, I invite you to check out those fonts. Even before this issue is fully fixed, many other issues have been addressed.
Just for the record, this issue has been addressed in the Libertinus fonts fork. Also there is a duplicate report of this issue at #336.