For example: in Sprint 2, on story, A Tester raises 4 bugs. 2 bugs got fixed in the same Sprint. The remaining 2 were pushed to the Product Backlog. At Sprint 6, we are picking those 2 bugs of story A to fix.
Do these 2 bugs need to be estimated for Sprint 6?
It depends on how you are using your estimates.
If your estimates are measuring the work delivered in a sprint then it makes sense to estimate the bugs.
If, however, you are using estimates to measure the team's ability to deliver completed, valuable functionality, then it makes sense to not include the estimate for carried over bugs.
Mike Cohn explains here how the approach you use determines how your team will use their velocity.
One thing to note is that the best possible approach is to avoid carrying bugs over across sprint boundaries. There are several things you can do to make this happen:
Estimation is a propogative of the team. The bugs if it is pushed to Product Backlog and in Sprint 6 it is pulled to be worked on by the team.Then it means you been able to estimated that the team can work on the bugs, right.
In agile you should practice zero-bug-policy. It can happen that the team could not fix the bugs immediately (Sprint2), but then do it in next sprint (Sprint3). If you waited so long (Sprint6) to deal with it, then you have to estimate it.
