Using sp_send_dbmail from a SQL-Agent job gives error EXECUTE permission denied.

Executed as user: domain\user1. The EXECUTE permission was denied on the object 'sp_send_dbmail', database 'msdb', schema 'dbo'. [SQLSTATE 42000] (Error 229). The step failed.

To solve this issue, execute the below line
ALTER DATABASE [SampleDB] SET TRUSTWORTHY ON

Ref: http://technet.microsoft.com/en-us/library/ms187861.aspx
http://blog.arjanfraaij.com/2011/06/using-spsenddbmail-from-sql-agent-job.html