Over the course of evolution, humans have become extremely good at one thing that really matters to evolution: ability to survive.
The strategy that we've chosen though is very different from what our fellow animals do. We are not stronger or faster. Our skin is not thicker. We are more fragile than most of other animals of similar size. In physically challenging situations we are very likely to die. But our strategy is to be one step ahead: we are very good at predicting and preventing (or avoiding) those situations.
The strategy of survival that has proven successful to us [so far] - is developing extraordinary ability to learn from previous experiences (first personal, later group experiences, then cultural) and predict what can go wrong in the future.
This may be good for survival, but definitely not so good for emotional wellbeing. Our ability to constantly live in multiple futures that can go wrong has robbed us of the ability to live in the now.
This very moment, if only you choose to pay attention to it, usually turns out to be safe and wonderful. But instead of focusing on enjoying it, our always-buzzing disaster predicting machines turn on to computing the next awful thing that has a minuscule chance of happening.
In this sense you can say that unhappiness (in the form of constant worrying) is a necessary byproduct of the kind of intelligence that has evolved to dominate in us.
So are we bound to unhappiness then? I don't think so. The trick is that we haven't [yet] lost our senses. Nor have we lost the parts of the nervous system that make us capable of living in the now. We simply don't associate the "self", the "I" with those parts.
The only thing that you need to do then is to slightly shift your center of consciousness from the worrying parts to the sensing parts.
After all, the choice of what you call yourself is yours at any given moment: do you want to be the worrying one who lives in the imaginary disastrous futures or would you rather be the sensing one who lives in the ever-pleasantly-surprising now?