I find some wine terms confusing, and I'm not just talking about truly weird stuff like "wet stone" and "boiled beef." What do you mean by "integrated oak?"
Thank you for not asking whether they actually put wet stones and boiled beef in wine (they don't!).
Wine critics often take liberties with language, leaving sane readers scratching their heads. One of my favourites (though I don't believe I personally have ever used it) is "melted licorice." I've not had the pleasure of sampling melted licorice, but I suppose that would be the flavour of licorice that's been sitting out in the sun.
"Integrated oak" is a little more technical. Oak-barrel maturation imparts a variety of flavours to wine, notably vanilla. Wood also can be astringent, prompting a dry sensation in the mouth. When well-integrated into the wine, the wood's flavours are subtler. You can sense vanilla, but in a way that complements the underlying fruit and never seems dominant or cloying.
Often an overtly oaked wine appears to lack sufficient fruitiness to support the lumber. It's sort of the oenological equivalent of a visible bra strap. It might work for Lady Gaga, but it's not the mark of a well-dressed wine.