$U(f,p)-L(f,p)< \varepsilon$v(A)

Question

Let $f:A ⊂ \mathbb{R}^n\to \mathbb{R}$ bounded, with $A$ a closed rectangle. so if there's a oscillation $o(f,x)< \varepsilon, \varepsilon>0, $ for all x that belongs to A. How can I show there is a partition P of A so: $U(f,p)-L(f,p)< \varepsilon$v(A) (with v(A) the volume of A )