This is a great question. Integration is a great concept and can help a company in many different ways. In light of this, let me give you a few suggestions of how integration can take place.
First, for there to be any sort of integration, communication is the first step. Hence, it would be important for a company to have the various department heads meet a few times a year to see what each are doing. This can create new ideas, synergism, and so many other ideas. For example, take the company Hyundai. They are a huge company with many parts - cars, shipping, electronics, and more. By integrating all of these sectors, they can help the company as a whole in so many ways.
Second, killing to birds with one stone is always a great exercise in efficiency. In light of this, it would be good to see if various departments can help each other in what they are already doing. For example, if one department ships merchandise to a particular location every week, then other departments can do the same without additional costs. This will also save on fuel costs, which can add up.