Guys, we know that $V(x_1)=-\int_{x_0}^{x_1}F(x)\,dx$ and $V(x_2)=-\int_{x_0}^{x_2}F(x)\, dx$. So we have
$$
V(x_1)-V(x_2)=\int_{x_0}^{x_2}F(x)\,dx-\int_{x_0}^{x_1}F(x)\,dx=\int_{x_0}^{x_2}F(x)\,dx+\int_{x_1}^{x_0}F(x)\,dx
$$
Now how do I know for sure that I can add these two integrals? Because I've learned that we need $c\in[a,b]$, such that
$$
\int_a^bf=\int_a^cf+\int_c^bf.
$$
For all we know we have $x_0<x_2<x_1$. How can I do the calculation in that case?
$$
\int_{x_0}^{x_2}F(x)\,dx-\int_{x_0}^{x_1}F(x)\,dx=\dots=\int_{x_1}^{x_2}F(x)\,dx.