For connecting to a sql server database via Windows authentication basically needs which server you want to connect , what is your database name , Integrated Security info and provider name.
Basically this works:
<connectionStrings>
<add name="MyConnectionString"
connectionString="data source=ServerName;
Initial Catalog=DatabaseName;Integrated Security=True;"
providerName="System.Data.SqlClient" />
</connectionStrings>
Setting Integrated Security field true means basically you want to reach database via Windows authentication, if you set this field false Windows authentication will not work.
It is also working different according which provider you are using.
SqlClient both Integrated Security=true; or IntegratedSecurity=SSPI; is working.
OleDb it is Integrated Security=SSPI;
Integrated Security=true throws an exception when used with the OleDb provider.