Introduction 1 Part 1: Introduction to Integration 3 Chapter 1: An Aerial View of the Area Problem 5 Chapter 2: Forgotten but Not Gone: Review of Algebra and Pre-Calculus 15 Chapter 3: Recent Memories: Calculus Review 37 Part 2: From Definite to Indefinite Integrals 51 Chapter 4: Approximating Area with Riemann Sums 53 Chapter 5: The Fundamental Theorem of Calculus and Indefinite Integrals 69 Part 3: Evaluating Indefinite Integrals 81 Chapter 6: Instant Integration 83 Chapter 7: Sharpening Your Integration Moves 91 Chapter 8: Here's Looking at u-Substitution 103 Part 4: Advanced Integration Techniques 115 Chapter 9: Integration by Parts 117 Chapter 10: Trig Substitution 131 Chapter 11: Integration with Partial Fractions 151 Part 5: Applications of Integrals 167 Chapter 12: Solving Area Problems 169 Chapter 13: Pump up the Volume -- Solving 3-D Problems 189 Chapter 14: Differential Equations 211 Part 6: Infinite Series 219 Chapter 15: Sequences and Series 221 Chapter 16: Convergent and Divergent Series 235 Chapter 17: Taylor and Maclaurin Series 255 Part 7: The Part of Tens 267 Chapter 18: Ten Mathematicians Who Anticipated Calculus before Newton and Leibniz 269 Chapter 19: 10 Skills from Pre-Calculus and Calculus I That Will Help You to Do Well in Calculus II 273 Index 279.