By the use of limits. I imagine you are familiar with that mathematical term.
You might be talking of two different things. Agrarian spoke of "surface with irregularly curved edges". You are talking of integrating "proper expressions". If no formula for the edge is known, calculus is no help, you are back to counting squares in a grid, like the first man.
In either case, I am talking about cardinal necessity of faith in any reasoning about the future, not about issues with precision. Newton (or Ptolemy, or Einstein) depend on faith not because they miss finer points of celestial mechanics, but because, like Aquinas said, in the Christian belief system the whole rig is going to poof, stop, while in most scientific belief systems it keeps turning forever.