Listen to shilolo here. There have been no proven results in living systems of antioxidants. The theory is very solid, but that is only sure in an isolated, simple system, of which the body certainly is not. We really can’t be sure of what antioxidants do when consumed in the long term, and in short term it probably has very little effect one way or another.
Keep in mind, though, that this is an extremely hard experiment to run. You’d need to track an independent group of people’s eating habits for decades to be sure of results, and antioxidant’s being added to food is a very recent thing. Mouse and other trials have been done, but as shilolo said, they’re pretty uninspiring.
As a last note, keep in mind that ‘dietary supplements’, such as antioxidants, ‘energy’ supplements, and really anything they put in food and claims will help cure something or other, is not approved by the FDA, they can say whatever they want, they need no proof. If you can’t prove conclusively that it doesn’t do what they say, which is incredibly hard, they get to keep on saying it. So, yeah. Take those things with a grain of salt.