Answer
$\int_C F\cdot n \ ds$
Work Step by Step
The expression for the flux $\phi$ of a vector field $F$ along a smooth oriented curve $C$ can be written as:
$\phi=\int_C F\cdot n \ ds$
where, $n = T \times k$ defines the unit vector and $T$ is called as the tangent unit vector.
So, our answer is: $\int_C F\cdot n \ ds$
