This video introduces the Fundamental Theorem of Calculus Part 2, which says that the area under a function between points a and b is obtained by evaluating the antiderivative of that function at the endpoints a and b. This is mindblowingly easier than using Riemann sums and limits to find areas.
An introductory example is also given to find the definite integral of x + sqrt(x) between 0 and 1.