Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X : \Omega \to \mathbb{R}$ is a D3161: Random real number on $X$
(ii)	$F_X : \mathbb{R} \to [0, 1]$ is a D205: Probability distribution function for $X$

Let $a, b \in \mathbb{R}$ each be a D993: Real number such that

(i)	\begin{equation} a \leq b \end{equation}
(ii)	$(a, b] \subseteq \mathbb{R}$ is a D1278: Right-closed real interval

Then \begin{equation} \mathbb{P}(X \in (a, b]) = F_X(b) - F_X(a) \end{equation}