Connect to SQL Server with Windows Authentication in a different domain

Question

I am trying to connect to a remote SQL Server on a VPN in a different domain. When I enter the Server name on the SQL Server and choose Additional Connection Parameters to add some extra stuff needed by my school:

Integrated Security=SSPI; User ID=DOMAIN\username; Password=Password

I get the following error:

Login failed. The login is from an untrusted domain and cannot be used with Windows authentication.