So in differential calculus we have the concept of the derivative and I can see why someone would want a derivative (to get rates of change). In integral calculus, there's the idea of a definite integral, which is defined as the area under the curve. Why would Newton or anyone be looking at the area under a graph? There seems to be no practicality in computing the area under the graph (other than the fundamental theorem of calculus which relates the two fields). I guess my question is what was the motivation behind the idea of a definite integral because Newton couldn't have known about the fundamental theorem of calculus beforehand.