Something like this might work if you are looking for problems in a specific sprint with a certain status:
project = MYPROJECT AND status = Closed and sprint in (mysprint)
Please note that this may also include issues that were part of several sprints and closed in a later version than mysprint.
If you are really interested in issues that were closed during a certain period, use something like:
project = MYPROJECT AND status CHANGED TO closed DURING (2016-07-01, 2016-07-15)
Dates in the format YYYY-MM-DD.
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