This book is based on Professor Williamson's twenty-six years of teaching calculus at the University of California, San Diego. It is a revised and updated version of a "tutors' guide" that he handed out to students wanting to tutor for his classes in integral calculus. Mostly, these tutors were a great help. But when they made mistakes in explaining technique or concept, these mistakes were hard to detect and rectify before the final exam. Tutoring Integral Calculus covers and hopefully rectifies the most common sources of tutoring difficulties.