Everyone with a thorough knowledge of single variable calculus knows that integration can be used to find the length of a curve on a given interval, called its arc length. Fortunately, if one endeavors to pose and solve more interesting problems than simply computing lengths of various curves, there are techniques available that do not require an extensive background. The purpose of this article is: (1) to alert the interested readers to an existing tool that appears in various calculus texts, called the arc length function, (2) to introduce the reader to a generalization of this function, called a measuring function, and (3) to tackle some new and interesting arc length problems using these two methods. (Contains 6 figures.)