Tobias Holck Colding continues MIT's 18.100B Real Analysis course with a lecture proving that continuous functions are integrable. He starts by defining uniform continuity, a stronger condition than ordinary continuity, and shows that any continuous function on a closed and bounded interval satisfies it. From there he builds the argument that such functions have a well defined integral, meaning the area under their graph is well defined. The eighty minute session works through the logical chain step by step, from compactness to uniform continuity to integrability, in the chalkboard proof style typical of MIT OpenCourseWare's upper level math lectures. It assumes familiarity with earlier course material on continuity and compact intervals and is aimed at students already following the full semester sequence.