Moving only SP 2010 SSRS integration to a different SQL server

Fairly self-explanatory. I have a SP 2010 farm that is currently set up to use SQL Server 'A' in integrated mode for Reporting Services. I have a new SQL server 'B' (same ver) that is also set up in SP integrated mode for RS. I want to simply stop using SSRS 'A' and start using SSRS 'B.'

I'm unclear how best to do this. Do I simply go into the Reporting Services Integration in Central Admin and enter the new information? Or do I choose 'add a server to the integration' to add server 'B' and then somehow drop server 'A'? Do I need to physically migrate any databases?

This has nothing to do with any content or SP databases - I simply want to move the SSRS integration.