Am I responsible for capital gains on inherited funds of sold property?

In most cases, the trustees receive a stepped up cost basis equal to the value of the asset on the day of the previous owner's death.  Interest, dividends and capital gains after the date of death will be taxable to the beneficiaries of the trust.

In other words, money in a bank account is not taxable when it is distributed.  Interest paid before the date of death is taxable to the deceased and interest paid after the date of death is taxable to the beneficiaries/grantees.  If the trust owns a house, and sells it, the trust uses a stepped up basis, so any capital gains are likely to be minimal, but if there are gains, the gains are taxable to the beneficiaries/grantees (but not the entire proceeds).