The question seems to refer to a connection between (part of) the fundamental theorem of calculus and Stokes' theorem in $n$-dimensional space.
If the real valued function $f(x)$ has an antiderivative $F$ on $[a,b]$, that is $f(x) = F'(x)$, then
$\int_a^b f(x) dx = F(b)-F(a).$
More suggestively,
\begin{equation*}
\int_a^b F'(x) d x = F(b) - F(a),\tag{1}
\end{equation*}
the integral of the derivative over the interval can be found knowing only the value of the function at the boundary of the interval.
Stokes' theorem is a generalization,
\begin{equation*}
\int_M d\omega = \int_{\partial M} \omega.\tag{2}
\end{equation*}
This theorem says that we can find the integral of the exterior derivative of the form $\omega$ over the $n$-dimensional manifold $M$ by integrating the form over the boundary $\partial M$ of the manifold.
If you don't know what a form is, never mind. It is our $F$.
And $d$ is our derivative.
And $M$ is our volume.
Equation (2) is totally analogous to (1), we are finding the sum of the derivative of some object over a volume knowing only the value of that object on the boundary.
An appropriate response to this result is amazement.
When we say that Stokes' theorem is a generalization of (1) we mean that for $n=1$ it is (1).
(1) is a special case.
Another special case of Stokes' theorem is the divergence theorem in three-dimensional space,
$$\oint_V \nabla\cdot {\bf F}\, dV = \oint_{\partial V} {\bf F}\cdot d{\bf S}.$$
If you continue on in physics you will learn very well this and other related results in multidimensional calculus in a good course on electromagnetism.
Rather than say more about the divergence theorem, we give below a summary of the important analogies between the various theorems.
$$\begin{array}{llcccccc}
&
\textrm{Theorem}
& \textrm{Dimension}
& \textrm{Object}
& \textrm{Derivative}
& \textrm{Volume}
& \textrm{Surface} \\ \hline
\textrm{Stokes'}
& \int_M d\omega = \int_{\partial M} \omega
& n
& \omega
& d\omega
& M
& \partial M \\
\\
\textrm{Fund. Thrm.}
& \int_a^b F'(x) d x = F(b) - F(a)
& 1
& F(x)
& F'(x)
& [a,b]
& a,b \\
\\
\textrm{Divergence}
& \oint_V \nabla\cdot {\bf F}\, dV = \oint_{\partial V} {\bf F}\cdot d{\bf S}
& 3
& {\bf F}
& \nabla\cdot {\bf F}
& V
& \partial V \\
\end{array}$$