To integrate two things is to put them together to form something new. What this definition leaves out is that integration normally means that each of the two things retains integrity: in integration the parts remain themselves and become part of a whole.
When we integrate sensory information with intuition and reason, we do blur the lines between thinking and sensing, or between real and imagined. What we do is to take what we know through our senses, what we know through our reasoning, what we know without knowing why we know it, and the information itself and put them all together. Each kind of knowing remains intact, and something is also formed that becomes our response to the information.
Each of us is the product of integration: we are made up of numerous 'selves' that exist in time and through time. This is not wildly metaphysical: we have eyes that see in particular ways and we add to them the ability to use language in particular ways, and certain kinds of skills and capabilities, and the memory we have of ourselves at different times and places. All of these work together to give us a sense of who we are. The whole is more than the sum of its parts - we become a unified self - and each of the parts functions within the whole system only because it retains its integrity (so we know the difference between a memory and current experience, for example).
Integration works when diverse parts come together and form something bigger without losing their integrity. How does that sentence change your response to being part of a couple or a group or a team?