The Logical Framework For Definite Integrals

Lesson Summary: 
In this lesson we are going to go through the logical framework that defines a definite integral. The main goal of this lesson is to show that when \[\lim_{||P\,||\to 0}\,L(P)\] and \[\lim_{||P\,||\to 0}\,U(P)\] are equal, then they are equal to \[\int_a^bf(x)\,dx.\] We also provide three equivalent definitions of a definite integral.