You can navigate to an open task to complete/close it from any Open Activities related list
Navigate to Activity Tab
Go to the Activities Tab
Activity List View
Navigate to the activity record you wish to close.
Click Edit
Closing Task from the Activity Record
1. Change the Status to completed (or what ever your organization uses to denote CLOSED)
2. Click the SAVE button
Close an Event
Only upcoming events display in the Calendar section.
Once the event date has passed, the event automatically displays on the Activity History related list.