Kurtz and Swartz (both New Mexico State U.) introduce a broad selection of integration theories focusing on the integrals named in the title. They present classical problems in integration theory in historical order to show how new theories were developed to solve problems that earlier ones could not handle. The detail of discussion varies from integral to integral. The four chapters are independent, and each contains 30-60 exercises to make it usable as a text in an introductory real analysis course