Login to SQL Server using Windows Authentication

The only change required is in the connection string: remove the User ID=...; and Password=...;, and add Integrated Security=SSPI; instead.

More information can be found here.

You need to modify your connection strings to follow the below format for a Trusted Connection:

Data Source=myServerAddress;Initial Catalog=myDataBase;Integrated Security=SSPI;

And then run your application in the security context of the domain user.