Before revision: We compute the improved bounds on the copula of a bivariate random vector  when partial information is available, such as the values of the copula on the subset of [0,1]^2, or the value of a functional of the copula, monotone with respect to the concordance order.
After revision: Improved bounds on the copula of a bivariate random vector when partial information is available, such as the values of the copula on the subset of [0,1]^2, or the value of a functional of the copula, monotone with respect to the concordance order.