Introductory calculus : understanding the integral

Content: 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 --