Derivation of work done by real gas According to the Wikipedia on real gases, it is stated that the expansion work done by a real gas differs from the ideal gas by $\int\left(V-\frac{RT}p\right)\,\mathrm dp$.

Firstly, does this mean $W_\text{real} = W_\text{ideal} + \Delta W$ or $W_\text{real} = W_\text{ideal} - \Delta W$?

Secondly, how is this formula derived?
For a reversible process in a closed system (no mass entering or leaving), the general equation for the expansion work done by a real gas on the surroundings is the same for an ideal gas, namely 
$$W = \int p\,\mathrm{d}V$$
However, for a real gas, we use the equation of state for that gas $p=p(n,V,T)$ rather than $p=\frac{nRT}{V}$, the equation of state for the ideal gas.