This document discusses different methods for calculating areas bounded by curves, including: 1) The left rectangle method and midpoint rectangle method which approximate areas by rectangles. 2) The disk/washer method which uses disks/washers to calculate areas. 3) The shell method which calculates volumes by shells. It also provides examples of using these methods, such as finding x-intercepts, graphing curves, setting bounds by solving equations equal to each other, and calculating integrals over intervals.