You can filter the full case database by date range using the Case Date Range filter in the Database Filters panel.
Details
The Database Filters panel queries your complete case history, including closed and previously actioned cases that are no longer visible in the default table view. This makes it the right tool for looking up cases within a specific date range, regardless of their current status.
To filter cases by date range:
Go to Cases in the main navigation.
Click Filters in the toolbar at the top of the page.

The Database Filters panel opens on the left side of the screen.
Click the Case Date Range field (labelled "Pick a date range").
A dual-month calendar appears. Click a start date, then click an end date to select your range.

Click Apply.
The resulting case view will display all cases for that required date range.
For an interactive walk-through, click the blue flashing circles below.
Clearing the date range filter
To remove the filter, open the Database Filters panel, clear the date range field, and click Apply again. You can also click Reset in the Cases toolbar to clear all active filters at once.