1. Using the integral in the approximation of area -- The summation notation -- The area under the graph of a function -

2. Understanding the concept of the integral -- The Riemann integral and signed area -- The integrals of piecewise continuous functions -- The precise definition of the integral --

3. Introduction to the fundamental theorem of calculus -- The fundamental theorem of calculus (part 1) -- The proof of theorem 1 -- The indefinite integrals of basic functions -- A short list of antiderivatives -- The fundamental theorem of calculus and one-dimensional motion --

4. The antiderivative and the fundamental theorem of calculus -- Some properties of the integral -- The second part of the fundamental theorem --

5. The indefinite and definite integrals of linear combinations of functions -- The linearity of indefinite and definite integrals -- The area of a region between the graphs of functions --

6. Using the substitution rule for integrals -- The substitution rule for indefinite integrals -- The substitution rule for definite integrals --

7. The fundamental theorem of calculus and the differential equation y' = f' -- The differential equation y' = f and the fundamental theorem -- Acceleration, velocity and position --

Index.