Email option in Delivery Extension is not available in SharePoint 2013 integrated Mode
As you already know Report Server can be run either in Native mode or SharePoint integrated mode.
Report server has a feature of scheduling subscriptions for your reports. Report Subscription allows you to schedule your reports to deliver to recipients.
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There are few Delivery mechanisms available in SharePoint.
- Windows File Share
- SharePoint Document Library
- Null Delivery Provider
There might be a situation that you cannot find the Email option in the list.
What you need to do is configure Email in Report Server Application.
How to Configure Email server for reporting server
Go to Central admin and then go to Manage Service Applications
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Then find the related Reporting Server Service Application and click on SQL Server Reporting Services Service Application
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Go to Email Settings section
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Enter you SMTP server details.
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Save the settings.
Now you can find the Email delivery option in the subscription settings.