Fundamental Theorem of Calculus

Fundamental Theorem of Calculus Although the notion of area is intuitive, its mathematical treatment requires a rigorous definition. This post introduces the Riemann integral, and proves the fundamental theorem of calculus—a beautiful result that connects integrals and derivatives. Riemann integral § Given a bounded1 1 Note that continuity is not required here; boundedness alone ensures the subinterval infima and suprema are finite. function \(f:[a,b]\to\mathbb{R}\), we can approximate the area.