This is an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if F is differentiable on the interval a, b], then F ]1 integrable on a, b] and f ]b a = F(b) - F(a). One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed carefully from their...