Biblical infallibility is the belief that what the Bible says regarding matters of faith and Christian practice is wholly useful and true. It is the "belief that the Bible is completely trustworthy as a guide to salvation and the life of faith and will not fail to accomplish its purpose. Some equate 'inerrancy' and 'infallibility'; others do not."
Infallibility and inerrancy 
From dictionary definitions, Frame (2002) insists that "infalliblity" is a stronger term than "inerrancy." "'Inerrant' means there are no errors; 'infallible' means there can be no errors." Yet he agrees that "modern theologians insist on redefining that word also, so that it actually says less than 'inerrancy.'"  Some denominations that teach infallibility hold that the historical or scientific details, which may be irrelevant to matters of faith and Christian practice, may contain errors. This contrasts with the doctrine of Biblical inerrancy, which holds that the scientific, geographic, and historic details of the scriptural texts in their original manuscripts are completely true and without error, though the scientific claims of scripture must be interpreted in the light of the phenomenological nature of the Biblical narratives. For example, Davis suggests "The Bible is inerrant if and only if it makes no false or misleading statements on any topic whatsoever. The Bible is infallible if and only if it makes no false or misleading statements on any matter of faith and practice."  In this sense it is seen as distinct from Biblical inerrancy, but always accompanying it. The Chicago Statement on Biblical Inerrancy uses the term in this sense, saying, "Infallibility and inerrancy may be distinguished but not separated."
Biblical integrity 
The idea of biblical integrity strengthens the concept of infallibility by suggesting that current Judeo-Christian biblical text is complete and without error (inerrant). The proposal suggests that the "integrity" of Biblical text—to include its present day message, purpose, and content—has never been corrupted or degraded.
There was a controversy during the Second Vatican Council on whether the Roman Catholic Church taught infallibility or inerrancy. Since then, the dispute has continued over how to interpret the dogmatic constitution Dei Verbum.
See also 
- McKim, DK, Westminster dictionary of theological terms, Westminster John Knox Press, 1996.
- Frame, John M. "Is the Bible Inerrant?" IIIM Magazine Online,Volume 4, Number 19, May 13 to May 20, 2002 
- Geisler & Nix (1986). A General Introduction to the Bible. Moody Press, Chicago. ISBN 0-8024-2916-5.
- Stephen T. Davis, The Debate about the Bible: Inerrancy versus Infallibility (Westminster Press, 1977), p. 23.
- Chicago Statement on Biblical Inerrancy, Article XI