You need to enter both boxes. Qualified Dividends in box 1b is only the portion (or all) of the amount in box 1a that may be eligible for capital gains rates. It is included in box 1a. So it is taxed at a lower rate.
Even though it shows up as income on the first page,if you have capital gains or qualified dividends the tax is not taken from the tax table but is calculated separately from schedule D. The tax will be calculated on the Qualified Dividends and Capital Gain Tax Worksheet. It does not get filed with your return.
