Integrity

Integrity effectively means ensuring that data or communications are 'unaltered'. In the context of security, integrity doesn't cover alteration of data or interactions because of nonmalicious, unintentional errors. Taking care of those is the job of error recovery on a local or network scale. Instead, integrity means ensuring that data or communications aren't tampered with. For example:

A user has accessed certain system resources. Preserving integrity means that they can't claim that they didn't. History can't be rewritten. Support for auditing the exercising of access rights ensures this.
A user has sent a message. Preserving integrity means that they can't claim it wasn't them; actions can be uniquely attributed to the entity that initiated them. Signatures are valid. The technical name for this issue is nonrepudiation.
A user sends data, that gets modified en route to the receiving party. Preserving integrity means that the modification can't go unnoticed. You can't change somebody else's letter with impunity! 'Message tampering' activities are detected.

In this context, even authentication can be construed as an aspect of integrity. It preserves the integrity of presenting an identity.