This document discusses the concept of the definite integral in calculating distance traveled given a velocity-time graph. It explains that the definite integral provides an exact value for distance by calculating the area under the velocity-time curve between two time points, while upper and lower estimates can be found by using the greatest or least values in places where the graph is ambiguous. Students are assigned problems from their textbook involving calculating distance using integrals or upper and lower estimates from velocity-time graphs.