Notice that the goal is not to provide the student with a set of computational techniques and procedures for solving a set of predefined problems. Rather, the emphasis is on the fundamental concepts and how they relate to each other. Computation is an important part of this process, but it is not the only one, nor is it the primary one. Students who approach this course assuming that "the answer" is the only thing that counts will find it frustrating and are not likely to do well.
The material to be covered includes: the definite integral, antiderivatives and the indefinite integral, the Fundamental Theorem of Calculus, integration techiques, applications of integrals, logarithms and exponential functions, inverse trigonometric functions, and improper integrals. See the the course outline for more details.
Math 13 covers material that normally would be covered in two terms of college calculus (Math 10 and Math 12), but since the students taking Math 13 all have had some calculus in high school, we will cover this material in one term, so expect the course to move quickly. On the other hand, don't make the mistake of thinking that since you have already seen some of the material that you can skimp on homework or class attendance. We will be giving a different level of detail and a different emphasis from what you probably had in high school, so you should definitely have something new to learn.