by Douglas S Kurtz (New Mexico State University, USA) & Charles W Swartz (New Mexico State University, USA)

This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock–Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.

• Riemann Integral
• Convergence Theorems and the Lebesgue Integral
• Fundamental Theorem of Calculus and the Henstock–Kurzweil Integral
• Absolute Integrability and the McShane Integral