Looking at the title of your post, it could be argued that we are both the sum of our lives, and the parts. Let's take a look:

What did you do at exactly 12:22pm, on the 21st of May, 2009? Now most people wouldn't remember something that specific, unless an event caused that moment to stand out in time, yet what happened in that moment caused part of your experience to develop, to exist in a particular way.

If exposure to life included your sense of self (sensory input, thoughts, choices and actions) no matter how slight, then it became personal experience, and as we cannot readily delete ourselves from our own experience, only play with the distance from it, and the value given to such a thing, then in one way, we are the sum.

Now try to imagine solving an issue, like the changing of a wheel on a car. If your mind flooded with memories while you were attempting to change that wheel, then it would be chaos and possibly dangerous, all those thoughts colliding: how to bake a cake, the taste of coffee, that website with a sale on, the smell of the cut grass nearby. Instead of allowing experience to flood the mind in the moment, we attempt to filter through experience to find what is the most applicable to the issues of the moment, and because of that, we are also the parts of our lives.

The sum of our lives are the resource, and the parts of our lives are the application, both the same thing, merely from a different perspective, with that perspective being the reflection of life, against values, habits, and context. Neither the sum, or parts actually equal the value of life that's found, the reason for living, because that's another entirely different question.

Here's a question that I have for you: what happens to trust in a poly relationship?

Asking because It's not something I would ever know about. What happens to trust, not just a trust that they'll return to you, I mean the trust found in that peaceful repose, that of a love that's found, the empty silences that are full, surely that must change, because that's built on a sense of completion, not the desire for someone else?