Preface.- 1. Introduction.- 1.1 The Riemann Integral.- 1.2 An Example of Riemann Integration.- 1.3 The Lebesgue Integral.- 1.4 'Interesting' and 'Inside'.- 1.5 An Example of a Trick.- 1.6 Singularities.- 1.7 Dalzell's Integral.- 1.8 Where Integrals Come From.- 1.9 Last Words.- 1.10 Challenge Problems.- 2. 'Easy' Integrals.- 2.1 Six 'Easy' Warm-ups.- 2.2 A New Trick.- 2.3 Two Old Tricks, Plus a New One.- 2.4 Another Old Trick: Euler's Log-Sine Integral.-...