Ok! So I know Newton and Leibniz invented Calculus independently and today a major part of maths requires calculus. So what mathematics was done BEFORE Newton?? (I mean the type of research.) Any history book suggestions would be priceless. Also there are methods of integration taught like integration by partial fraction and integration by parts etc. Later I found there was a topic in higher algebra by hall and knight about partial fractions. So that topic belongs to algebra first and later applied to evaluate integrals so I'm guessing whatever calculus we learn the basic algebraic and trigonometric (And geometric?) foundation was available to him so defining differentiation and integration was the most crucial part? Did he define integration as limit of sum?? More question on the same topic are welcome provided they don't drag the thread towards philosophy (moderators are there to take care of that ) . I will add more if If more questions pop in !!!