## Properties of the Definite Integral

Read this section to learn about properties of definite integrals and how functions can be defined using definite integrals. Work through practice problems 1-5.

### Properties of the Definite Integral

Definite integrals are defined as limits of Riemann sums, and they can be interpreted as "areas" of geometric regions. These two views of the definite integral can help us understand and use integrals, and together they are very powerful. This section continues to emphasize this dual view of definite integrals and presents several properties of definite integrals. These properties are justified using the properties of summations and the definition of a definite integral as a Riemann sum, but they also have natural interpretations as properties of areas of regions. These properties are used in this section to help understand functions that are defined by integrals. They will be used in future sections to help calculate the values of definite integrals.