To give you a bit of context, if I'm trying to calculate the work done by a force from a distance $x_0$ (given constant) to $x$ (variable), I've been told (in lectures) to write the work done as $$W=\int_{x_0}^x F(\xi)d\xi \tag{1},$$ rather than $$W=\int_{x_0}^xF(x)dx \tag{2},$$ the reason being that "we've got the same variable in two places".
But what exactly is wrong with this?
Is $(2)$ wrong?