If a vector function $\vec F: \mathbb R^3 \to \mathbb R^3$ is given, and $\vec F=\vec F(\vec x)$, where $\vec x$ denotes position and $\vec x=\vec x(t)$, we define the integral $$I=\int_{C}\vec F \cdot d\vec x=\int^{t_b}_{t_a}\vec F(\vec x(t)) \cdot {d\vec x \over dt} dt \tag{1}$$ If we parametrize $C$ using the arc length $s$ of the curve then we can write $$\int_{C}\vec F \cdot d\vec x = \int_{C} (F_1dx+F_2dy+F_3dz)=\int_{C}\vec F \cdot d\vec s \tag{2}$$
My question:
Why can replace $d\vec x$ by $d\vec s$ in equation $(2)$?
What is the meaning of $d\vec s$ given that $s$ is the arc length and hence a scalar?