For the DFA given in question :
1) We can see that its looping on state 1 for b so we use : b* {Scan all the b's and stay at same state}
2) By scanning a we move to a final state hence we use 'a'
3) Now since weather we scan an 'a' or 'b' we stay at final state hence we use (a+b)* {Universal set}
4) The dead state given in the DFA is not reachable in any way hence we ignore it.
Final RE obtained b*a(a+b)*