N-CSR Item 12(b) - Exhibits: Certifications

                            SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C.ss.  1350,  the  undersigned  officers of Federated  Income
Securities Trust on behalf of Federated Capital Income Fund (the  "Registrant"),
hereby certify,  to the best of our knowledge,  that the Registrant's  Report on
Form N-CSR for the period ended November 30, 2004 (the "Report")  fully complies
with  the  requirements  of  Section  13(a)  or  15(d),  as  applicable,  of the
Securities  and Exchange Act of 1934 and that the  information  contained in the
Report fairly presents,  in all material respects,  the financial  condition and
results of operations of the Registrant.


Dated: August 15, 2005

/s/ J. Christopher Donahue

Title: President, Principal Executive Officer



Dated: August 15, 2005

/s/ Richard J. Thomas

Title: Treasurer, Principal Financial Officer

This  certification is being furnished solely pursuant to 18 U.S.C.ss.  1350 and
is not being filed as part of the Report or as a separate disclosure document.