Explores the critical contributions by Riemann, Darboux, Lebesgue, Henstock, Kurzweil, and Stieltjes to the theory of integration, and provides a glimpse of more recent variations of the integral such as those involving operator-valued measures.

C. Ray Rosentrater is a Professor of Mathematics at Westmont College, California, where he has also served as Department Chair and Associate Dean for Curriculum. He has been recognized as Westmont's Teacher of the Year in the Natural and Behavioral Sciences and has received the Faculty Research Award.

Preface; 1. A historical introduction; 2. The Riemann integral; 3. The Darboux integral; 4. A functional zoo; 5. Another approach: measure theory; 6. The Lebesgue integral; 7. The gauge integral; 8. Stieltjes-type integrals and extensions; 9. A look back; 10. Afterword: L2 spaces and Fourier series; Appendices: a compendium of definitions and results; Index.