What is Integration? Finding the Area Under a Curve

The video tutorial introduces integral calculus, explaining its historical development and its relationship with differentiation. It describes integration as finding the area under a curve, using rectangles to approximate this area. The tutorial demonstrates this with the function y = x^2, showing how increasing the number of rectangles improves the approximation. It introduces summation notation to represent the sum of areas and explains the connection between integration and differentiation, highlighting Newton's contribution to calculus.

What is the significance of using an infinite number of rectangles in integration?

How can the area under the curve of the function y = x^2 be calculated according to the text?

What is the final result for the area under the curve of y = x^2 from 0 to 1?