Service_ID  Service_RNO Cust_Name   Agrement_ID Cust_ID Service_Date    Next_Service
4                004    customer1   35           16     2016-01-03      2016-02-02
5                005    customer2   35           16     2016-02-03      2016-03-01

SELECT  dbo.Service.Service_ID,
        dbo.Service.Service_RNO,
        dbo.Customer.Cust_Name,
        dbo.Service.Agrement_ID,
        dbo.Customer.Cust_ID,
        dbo.Service.Service_Date,
        dbo.Service.Next_Service
FROM dbo.Service
INNER JOIN dbo.Customer ON dbo.Service.Cust_ID = dbo.Customer.Cust_ID
WHERE  Next_Service between '2016-02-01' and '2016-02-06'
AND    Next_Service not in (
          SELECT Dateadd(d, 1, Service_Date)
          FROM Service s
          WHERE s.Cust_ID = dbo.Customer.Cust_ID
)
ORDER BY Next_Service

SELECT  dbo.Service.Service_ID,
        dbo.Service.Service_RNO,
        dbo.Customer.Cust_Name,
        dbo.Service.Agrement_ID,
        dbo.Customer.Cust_ID,
        dbo.Service.Service_Date,
        dbo.Service.Next_Service
FROM dbo.Service
INNER JOIN dbo.Customer ON dbo.Service.Cust_ID = dbo.Customer.Cust_ID
WHERE  Next_Service between '2016-02-01' and '2016-02-06'
AND    Next_Service not in (
          SELECT Dateadd(d, 1, Service_Date)
          FROM Service s
          WHERE s.Cust_ID = dbo.Customer.Cust_ID
)
or    Next_Service not in (
          SELECT Dateadd(d, 1, Service_Date)
          FROM Service s
          WHERE s.Cust_ID = dbo.Customer.Cust_ID
)
ORDER BY Next_Service