Much of the antioxidant content in carrots comes from its beta-carotene, which our body converts to vitamin A. Because of this, cooked carrots - whether they be boiled, baked, or steam - are still healthy for you, since they retain much of their antioxidant content. For example, baby raw carrots have an ORAC value of 436, which yes is 33% higher, but still demonstrates how a high amount of antioxidants continues to be present in the cooked carrots. Whole unpeeled carrots contain even more than both of these, but that's a bad comparison since most people peel and discard the outer skin, which like most vegetables, has a higher concentration of antioxidant content. Whatever form you consume them though, they're not a good overall source, as their ORAC is quite low relative to most other plant-based foods.
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010