What is the relationship betweeen a pdf and cdf? I am learning stats. On page 20, my book, All of Statistics 1e,  defines a CDF as function that maps x to the probability that a random variable, X, is less than x.
$F_{x}(x) = P(X\leq x)$
On page 23 it gives a function 
$P(a < X < b ) = \int_{a}^{b}f_{X}dx$
and then says that "the function $f_{X}$ is called the probability density function. We have that..."
$F_{x}(x) = \int_{-\infty}^{x}f_{X}dt$
I am a little confused about how to characterize the most important difference between them. The equation above says that the cdf is the integral of the pdf from negative infinity to x. Is it fair to say that the cdf is the integral of the pdf from negative infinity to x?

The cumulative distribution function $F_X$ of any random variable $X$ is defined by
$$
F_X(x)=P(X\le x)
$$
for $x\in\mathbb R$. If $X$ is a continuous random variable, then the cumulative distribution function $F_X$ can be expressed as
$$
F_X(x)=\int_{-\infty}^xf(x)\mathrm dx
$$
for $x\in\mathbb R$, where $f$ is the probability density function of a random variable $X$. If a random variable $X$ is not continuous, it does not have a probability density function (for example, a random variable with Bernoulli distribution).
