Subtraction of Probability Measures

Question

I have just read that apparently the following two conditions are equivalent: $$ \int f dP \geq \int f dQ \Longleftrightarrow \int f d(P-Q) \geq 0$$ for $f:\mathbb{R}^n\longrightarrow\mathbb{R}$ and $P$ and $Q$ two probability measures on $\mathbb{R}^n$. Maybe I am missing some measure theory here but I can not see why this is true without further assumptions.