  The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett.
98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008)
042308] are proved by using two properties of the fidelity. In two-qubit
systems, for a given value of concurrence, the states achieving the maximal
upper bound, the minimal lower bound or the maximal difference upper-lower
bound are determined analytically.
