For exporting emails by date range from Outlook to Excel, please do as follows:

1. Shift to the Mail view, and open the mail folder where you will export emails by date range.

2. Type the search criteria received:2016/4/15..2016/5/10 into the Instant Search box.

Note: received:2016/4/15..2016/5/10 means searching emails received between 2016/4/15 and 2016/5/10, and you can change the date range as you need.  

3. Now all emails received in the specified date range are found out. Select all search results, right click and select Copy from the right-clicking menu. See screenshot:
Note: You can select all search results with clicking any one email in the mail list and pressing the Ctrl + A keys simultaneously.

4. Create a new workbook, select the Cell A1, and press Ctrl + V keys simultaneously to paste all search results into the new workbook.

5. Save the new workbook.

And now all emails received between the specified date range are exported to an Excel workbook.

If you need to export emails by specified date range to PST file in Outlook, please do as follows:

1. Click File > Open & Export > Import/Export (or File > Open > Import).

2. In the opening Import and Export Wizard, please click to select the Export to a file option, and click the Next button.

3. In the new Export to a File dialog box, please click to select the Outlook Data File (.pst) option, and click the Next button.

4. Now the Export Outlook Data File dialog box opens. Please click to select the mail folder which you will export emails from, and click the Filter button. See screenshot below:

5. Now in the popping Filter dialog box, please go to the Advanced tab, and specify filter criteria as:
(1) Click Filed > All Mail fields > Received;
(2) Choose between from the Condition drop down list;
(3) Type the date range into the Value box. In my case, I type 2016/4/15 and 2016/5/10 into the Value box.
(4) Click the Add to List button.
(5) Click OK > Next.

6. In the new opening Export Outlook Data File dialog box, click the Browse button to open the Open Outlook Data Files dialog box, next specify the destination folder you will place the PST file into, name the PST file in the File Name box, and then click OK > Finish.

7. In the new Create Outlook Data File dialog box, please click the OK button.
Note: If you need to add a password to the exported PST file, please type your password into both Password box and Verify Password box, and then click the OK button.

So far, we have exported the emails received in the specified date range to a separate PST file in Outlook.

Count the total number of search results in Outlook

Export search results in Outlook to PST/Excel file

Show full folder path of email search results in Outlook