line integral over differential explained in loose terms

Question

today I learned about exact and inexact differentials. There you often integrate the differential $dF(x,y)$ along a certain path $\gamma_1$ (here in 2D) like this $$ \int_{\gamma_1} dF $$ my question is now what is the difference between this and $$ \int_{\gamma_1}F(x,y)ds=\int_{a}^{b}F(\gamma_1(t))|\gamma_1'(t)|dt $$ where $\gamma_1: [a,b]\rightarrow \mathbb{R}^2$ (assuming that the differential is in 2D and exact. Otherwise there couldn't be an $F$ to integrate over obviously)
The second is a line integral of $F$. So it a sum over the values $F$ has along that path. But how can the first integral be explained in loose terms? Is it just the sum of the values of the derivative along the path?