Introduction to Integrals

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).