What is a Probability Density Function?
To find the probability that a continuous random variable lies in a range, we use its probability density function (PDF).
The PDF for the random variable $X$ is written $f_X$.
Since we find areas under a function by integrating, such probabilities are given by the following formula:
$\mathbb{P}(a \le X \le b) = \int_{a}^{b} f_X(x)dx \ \ , \ \ a \le b$.
Because $X$ must end up being equal to some real number, the total area under the PDF is equal to 1:
$\int_{-\infty}^{\infty} f_X(x)dx =1$.
PDFs also have to be non-negative everywhere, though they may be equal to 0.