From Integrations if I click the 
icon I get two options that are relevant here: Rename, and System Options.
When I configure an Integration I can also (often) choose to set its area, but I can’t do that on the integrations page after the integration has been configured.
On the device page I have a pencil icon, where I can change the name and set the area. But the system options are nowhere in sight.
This is related to Why the heck is Settings so confusing to navigate?, but is specific to the integrations area of HA.