Lecture 18: Integrable Functions

We will show that continuous functions are integrable. This means that the graph of such a function bounds a well-defined area. To do so, we define what it means for a function to be uniformly continuous. This is a strong version of continuity but we will see that all continuous functions on a closed and bounded interval have this stronger property. Once we have shown that all continuous functions on a compact interval are uniformly continuous, it will follow relatively easily that they are integrable.