In order to get both antioxidants and phytochemicals in a diet, you must either shop for food with the chemicals already in them or buy supplements.
An argument for taking supplements is for those who need chemicals supplementary to their diets, such as those who need more iron than would be possible while eating normally. Vegetarians and vegans who do not get enough VItamin B-12 from their diet without meat, for instance, need to supplement this in their diet as well as omega-3 fatty acids.
Since fruits and vegetables contain many phytochemicals and nutrients, an argument could be had that they supply chemicals you may not only need but not be able to gain from supplements.
Epidemiological evidence suggests a diet without saturated or trans fats, high in fruits, nuts vegetables, whole grains, and omega-3 fatty acids. It does not suggest the use of supplements.
Sometimes the benefits from phytochemicals and vitamins are more effective when coming from food rather than supplements. Research suggests that in order to get enough beta-carotene and Vitamin C to use as anti-oxidants all you need to do is have one glass or orange juice or carrot juice a day.
There are risks associated with the ingestion of supplements. There is a possible increased risk of coronary heart disease and lung cancer in smokers who consume Vitamin E and beta-carotene supplements while the risk is decreased if the same population obtained their Vitamin E from fruits and vegetables. Supplements containing a combination of anti-oxidants have shown to increase the risk of gastrointestinal cancer and coronary heart disease.