Math major, heavily quantitative studies / research thereafter.

Anyway, my point is really that the integration of injustice is not in itself clearly pointing towards justice. There are extreme cases, of which I gave two, where the integration result (as I understand it) seems to give a profoundly counterintuitive answer--"wrong", I would submit.

That would motivate me to ask why. What is it about what we've captured quantitatively that doesn't do justice to our intuitions?

I think there are three assumptions at least that seem to cause some problems:

(1) Injustices demand equal redress regardless of how far in the past they occurred. (This is in contrast to the idea of temporal discounting: https://www.behavioraleconomics.com/resources/mini-encyclopedia-of-be/time-temporal-discounting/).

(2) Injustices are inflicted at the level of the group and must be redressed at the level of the group regardless of how group size or individuals within the group change. (This is in contrast to founding principles of the country, e.g. https://www.archives.gov/founding-docs/declaration-transcript where all men not identity groups are created equal etc..)

(3) An acceptable redress for cruelty to one group is cruelty to another group that was previously treated better. (This is in contrast to the idea of human rights, where cruelty is always wrong.)

All of these are direct consequences of the way in which the integral is calculated (to the best of my understanding). But I think they all deserve a robust argument in favor, not just acceptance because they happened to be introduced with the mathematics, not freestanding.