Icicles does not do anything to "integrate with" Helm. Perhaps Helm does something to "integrate with" Icicles, but I doubt it.
More likely is that you loaded some other library (perhaps a Helm add-on someone wrote) that grabs some of the key bindings that Icicles uses by default.
If the only problem you have is key bindings then my suggestion would be to customize the bindings the way you like.
The place to start is
C-h k followed by the key you're interested in. That should tell you what command it is bound to, and what library/file it is defined in. If it does not tell you the file but it tells you only that the key is bound to command
some-helmish-whatever then search (e.g.
M-x grep) the source code of the libraries you use, to find out where it is defined, where it is bound to the key, and in what keymap it is bound to that key. You can then just unbind it from that keymap, if you want (i.e., bind it to
nil in that map).
If you don't easily find out which code is grabbing the Icicles bindings you want Icicles to have, or you don't want to try that, then an alternative is to make Icicles use different key bindings.
That is easy to do. There are Icicles user options for customizing each group of Icicles default keybindings. The Icicles doc, section Customizing Key Bindings tells you all about this.
If it is a top-level key that you're interested in, such as
C-x C-f, then the option to customize is
icicle-top-level-key-bindings. Just bind some other key to the command (
icicle-file) that Icicles binds by default to
Looking at the option value you can see that by default Icicles remaps vanilla Emacs command
find-file to Icicles command
icicle-file. In file
icicles-opt.el you'll see "`C-x C-f'" as a comment next to the line that does that.
So in this case, instead of Icicles explicitly binding (by default) key
C-x C-f to
icicle-file, it instead remaps all keys bound to command
icicle-file (while in Icicle mode).
If some other library (Helm or whatever) itself remaps
find-file first then there will be no keys bound to it for Icicles to remap. In that case, you can try changing the order of invocation, invoking
icy-mode before the other (e.g. Helm) mode. Or you can try the other way around.
But a simple alternative is to just add some other binding to
icicle-top-level-bindings, to use some key other than
C-x C-f for