Here we introduce the basic notions of integration, explore the connection between various kinds of integrals and look at some basic, important and useful properties of integrals.

- Riemann (definite) integral: Definition, explanation and examples.
- Properties of the Riemann integral.
- Newton integral (antiderivative): Definition, properties, and elementary integrals.
- The Fundamental Theorem of Calculus: connection between the above integrals.
- More properties of integrals.
- A note on other kinds of definite integrals (Newton definite integral, Lebesgue integral).