[Math] the point of finding the area under the curve

Question

I am learning calculus and am at the point where we switch from differentiation to integration. What is the point of finding the area of a certain graph under the curve?
So far I do understand and am learning how to find the area under the curve using Riemann sums but my teacher is not clear on what the point of it is.

Answer 1

The area under a curve is its integral. Many many physical, chemical, financial, and other variables are related by such integration. For instance if you have a speed as a function of time ($v(t)$), you can find the position $x(t)$ (up to a constant) by integrating the speed.