People have investigated antioxidants pretty thoroughly and supplemental antioxidants really aren&#x27;t needed in healthy cells.  <i>Power, Sex, Suicide: Mitochondria and the Meaning of Life</i> goes into some details on the biochemistry behind that but you can look at the Antioxidant Wikipedia page for all the research showing no positive effect.<p>If I were to speculate it might be that while normal cells can make enough for themselves cancerous cells benefit from external antioxidants.  The damage done by free radicals is mostly concentrated in the mitochondrial genome, which is why evolution has brought as many genes as possible out of the mitochondria into the nucleus.  By contrast the mutations that causes cancer are, IIRC, mostly inside the nucleus.