So I am doing a study on Riemann, and one of his big things is apparently the "Riemann integral".
My understanding is that this concept was meerly the first definition of a definite integral, and because of this definition it was possible to calculate things like displacement thus allowing physics to calculate displacement of a particle moving along a line with a specefic velocity. Is this accurate? Was this all his definition was? Was he really the first?
I just find it kinda odd that something that one would think was discovered when the integral was first defined actually came quite a bit later.
Newton and Leibniz separately developed the theory of integration and implicitly the notion of a definite integral, this was much earlier than Riemann, Riemann made the concept of integration more rigorous, including the concept of the definite integral.