entropy is a state variable. if the integral of a variable around any closed
path in a coordinate system is zero, then the value of that variable at a
point depends only on the coordinates of that point and not at all on the
path by which we arrived at that point. such a variable is often called a
state variable, meaning that it has a value that is characteristic only of
the state of the system, regardless of how that state was arrived at. the
difference in entropy between the initial state and the final state is
independent of the path we choose from the initial to the final state. even
though nature may have chosen an irreversible path between the initial and
the final state for the actual process, we can choose any convenient
reversible path for the calculation of the entropy change.

to understand line integrals is a good preparation to understand the law of
conservation of energy, the independence of path, and entropy as a state
variable.