I recently wrote about performing a bulk export of mailboxes to PST from a collection (https://deangrant.wordpress.com/2013/10/08/bulk-export-of-exchange-mailboxes-from-a-collection/), in this script the entire contents of the mailbox was exported.
However, in instances where you only require to export a particular date range, you can use the Content Filter switch as part of the New-MailboxExportRequest cmdlet in Microsoft Exchange.
For Example, if I was looking to export mail items for the previous calendar month, I could run the following:
New-MailboxExportRequest -Mailbox <Mailbox Name> -ContentFilter {(Received -le '30/09/2013') -and (Received -ge '01/09/2013')} -FilePath \\Server\Share\Mailbox.pst
This would export all mail items which are greater than or equal to 01/09/2013 and less than or equal to 30/09/2013.
This can be particular useful, if performing a large mailbox export where the approach could be to perform an initial export of all the data and then run incremental style exports by using the content filter.