Well, specifying an account for the data source is not a bad thing for many scenarii.
- This is necessary for being able to suscribe to a report (windows integrated security does not make sense for a report that is run unattended).
- Specifying an account is also the opportunity to provide limited access to SharePoint data in lists for which the user doesn't have the necessary permissions.
Regarding windows authentication in this case, you will have to implement Kerberos.
Regards,