Answer
These are the standard-output logs of the Integration/Connect server component. Their logging behavior — including the standard-output severity level, and whether standard output gets redirected into the regular server logs instead — is configurable through the IFS Middleware Server Admin Console; lowering the configured severity level reduces how much gets logged, which controls their growth going forward. It is generally safe to delete these existing files, since they're just informational output logs rather than required application state, but it's good practice to open and skim one in a text editor first to confirm there's nothing you specifically need before deleting.