Can a flux that varies only in $x$ through surface $ds$ be separated into $dx$ and $dy$ terms

Question

For a vector such as this, if $ds$ was vertical, it could be written as $F(x)dy$. However, as $ds$ varies with $x$, can it be written as a with respect to only $F(x)$, $dx$ and $dy$ terms? The general term is written as

$$\int^{ds}_0 F(x) dS$$ but that is where I'm stuck