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.
$\begin{array}{llcccccc} & \textrm{Theorem} & \textrm{Dimension} & \textrm{Object} & \textrm{Derivative} & \textrm{Volume} & \textrm{Surface} \\ \hline \textrm{Stokes'} & \int_M d\omega = \int_{\partial M} \omega & n & \omega & d\omega & M & \partial M \\ \\ \textrm{Fund. Thrm.} & \int_a^b F'(x) d x = F(b) - F(a) & 1 & F(x) & F'(x) & [a,b] & a,b \\ \\ \textrm{Divergence} & \oint_V \nabla\cdot {\bf F}\, dV = \oint_{\partial V} {\bf F}\cdot d{\bf S} & 3 & {\bf F} & \nabla\cdot {\bf F} & V & \partial V \\ \end{array}$