Properties of Definite Integrals

I have summarized the properties of definite integrals.

Reverse Interval

$$
\int_{a}^{b} f(x) dx = -\int_{b}^{a} f(x) dx
$$

Addition & Subtraction

$$
\int_{a}^{b} (f(x) ± g(x)) dx = \int_{a}^{b} f(x) dx ± \int_{a}^{b} g(x) dx
$$

Multiplication by a Constant

$$
\int_{a}^{b} cf(x) dx = c\int_{a}^{b} f(x) dx
$$

Interval Addition

$$
\int_{a}^{b} f(x) dx = \int_{a}^{c} f(x) dx + \int_{c}^{b} f(x) dx
$$