《积分：分析学的关键（英文）》共包含五章内容，主要介绍了分析学的关键——积分。首章阐述了积分在分析学中的重要作用，详细地论述了常用的积分理论，给出了积分的相关概念；第二章和第三章讨论了黎曼积分和勒贝格积分；第四章对两种理论进行了比较；最后一章介绍了Henstock积分、Daniell积分、Riemann-Stieltjeg积分等常用积分。通过论述常用的积分理论及应用等知识，让读者更深入地了解有关分析学在积分中的重要性。
　　《积分：分析学的关键（英文）》由浅入深，详略得当，条理清晰，可供高等院校师生及数学爱好者参考使用。

　　The integral is an old idea-a venerable part of the cakulus .The integralis important because（i）it is dual to the derivative（as the Fundamental Theorem of Cakulus tells us）and（ii）it is the most powerful and versatile tool in calculus. Most of real analysis is based on the theory of the integral. And the integral， in turn， inspires many of the key ideas of functional analysis.
　　There are many theories of the integral. One of the first modern theories was that enunciated by Bernhard Riemann in his celebrated paper on Fourier series. The Riemann integral is relatively simple， and it does the job nicely It is certainly the most ubiquitous and widely-used integral in the world today. Mathematicians， physicists， engineers， and many others use the Riemann integral regularly.

　　Steven G. Krantz，born in San Francisco, California in 1951. He received the B.A. degree from the University of California at Santa Cruz in 1971 and the Ph.D. from Princeton University in 1974.
　　Krantz has taught at UCLA, Princeton University, Penn State, and Washington University in St. Louis. He has served as Chair of the latter department.
　　Krantz has directed 9 Masters theses and 18 Ph.D. theses. He has been awarded the UCLA Alumni Foundation Distinguished Teaching Award, the Chauvenet Prize, and the Beckenbach Book Prize.
　　Krantz has published over 155 scholarly articles and over 55 books. He is currently the Editor of the Notices of the American Mathematical Society.