Functions Defined by Improper Integrals

William F. Trench, 2012. — 29 pages. This is a revised version of Section 7.5 of Advanced Calculus (Harper & Row, 1978). It is a supplement to my textbook Introduction to Real Analysis, which is referenced several times here. You should review Section 3.4 (Improper Integrals) of that book before reading this document.