You don't need to draw DFA for this problem .
If we see the regEx itself , on expanding.
$R=(a+b)^{*}ba+(a+b)^{*}b+(a+b)^{*}$.
Thus according to the regEx , the language accepted will be all the strings on $\sum^{*}$ concatenated with a 'b' , concatenated with 'a'.
All the strings of $(a+b)^{*}$ will be in either $(a+b)^{*}a$ or $(a+b)^{*}b$ .
So there must be 2 equivalence classes . Right?
But we've forgotten about $\epsilon$ ,since $\epsilon$ is also present in the language .
Thus , there are 3 equivalence classes.