Definite Integral Darboux Sum Epsilon Reformed Definition

Epsilon Reformed Defintion

1. Let $a,b\in R$
2. Suppose $a<b$
3. Suppose $f(x)$ is bounded on $[a,b]$
4. $\forall ϵ>0,\exists$ Partition P on $[a,b]$ s.t $U(f,P)-L(f,P)<ϵ$ This is more user friendly since all you need to do is pick a partition which has an upper darboux sum equal to the lower darboux sum