We briefly mention the history of integral calculus and mathematics in the ancient Greeks era in Sect. 6.1. In Sect. 6.2, we define integration, and we prove that a continuous function defined on a finite closed interval is integrable in Theorem 6.2.2. Then we finish up this section with the fundamental theorem of calculus. We introduce uniform continuity in Sect. 6.2 in order to prove that a continuous function on a closed interval is integrable in Theorem 6.2.2. However, we discuss uniform continuity further in Sect. 6.3. We give a brief review of the techniques of integration in Sect. 6.4.