Overview
The Riemann integral was one of the first and simplest integrals to be defined. An integral is a method that is designed to try to calculate the area underneath a curve.For example, consider the area underneath the following curve.
Properties
The Riemann integral is known to have the following properties.
Linearity
{% {\displaystyle \int }_a^b c_1f(x)+ c_2g(x) dx = c_1{\displaystyle \int }_a^b f(x) dx + c_2{\displaystyle \int }_a^b g(x) dx %}
Additivity
{% {\displaystyle \int }_a^b f(x) dx + {\displaystyle \int }_b^c f(x) dx = {\displaystyle \int }_a^c f(x) dx %}