>>14363843Integrals are a bit different. Either way you don't get the function from the area, you get it from the antiderivative which can be used to compute the area. Without this, all you can get are approximations (or you can use other fundamental calculus concepts in certain cases)
And even after all this, no matter how many points you have, summing up a bunch of linear equations isn't really going to help you. It will just get you another linear equation. You can combine them in more complex ways but again we are back to regressions, series', and interpolation methods, and none of these will be exact unless you already knew enough about the graph to conclude so.
Also last note that not every function can be written in the notation we have now. Some at best can only be described in differential form. I can draw a squiggle on a piece of paper and you won't be able to find a function because no (practical) relationship connects all the points on the squiggle together. Even if this sum method were to work for some graphs, it would not work as an algorithm for all possible graphs because some relationships just cannot be expressed in the way we've defined math
