Why We Never Actually Learn Riemann's Original Definition of Integrals - Riemann vs Darboux Integral

We typically credit Riemann for his discovery of integrals. However, in school, we never actually learn the actual Riemann Integral as he invented. Instead we learn the “Riemann“ Integral, which is actually the Darboux Integral. Why is that? In this video, we uncover the truth behind the two different definition of integrals. Links: Formal Definition of Supremum and Infimum Why Sup and Inf Always Exist Proof That the Lim of Upper Sum = Inf of Upper Sum #93f948 Integrability of Monotone and Continuous Functions Integrability of Monotone and continuous Chapters: 00:00 Intro 01:24 Rigorous Foundations of Calculus 02:06 Different Types of Integration 02:48 Generalized Riemann Sum 04:08 Riemann Integrability 04:49