You can specify connection string via ConnectionString
parameter:
Update-Database -ConnectionString "data source=server_name;initial catalog=db_name;integrated security=True;MultipleActiveResultSets=True;App=EntityFramework" -ConnectionProviderName "System.Data.SqlClient" -Verbose
Also you need to use this parameter with the same value for Add-Migration
command:
Add-Migration Version_Name -ConnectionString "data source=server_name;initial catalog=db_name;integrated security=True;MultipleActiveResultSets=True;App=EntityFramework" -ConnectionProviderName "System.Data.SqlClient" -Verbose