This paper develops a novel integrated learning and optimization (ILO) methodology to solve the economic distribution (ED) and DC optimal power flow (DCOPF) problems to improve economic operation. The optimization problem for ED is formulated with load as an unknown parameter, while DCOPF consists of load and power transfer distribution factor (PTDF) matrix as unknown parameters. PTDF represents the incremental change in the actual power of a transmission line due to the actual power transfer between two regions. It represents a linearized approximation of the power flow through the transmission line. In this paper, we develop a novel ILO formulation to solve the post-penalty, power market, and line overload problems using the ED and DCOPF optimization formulations. The proposed methodology trains the regret function by capturing the real-time power market and line overload behaviors, and eventually trains the unknown load and line PTDF matrix on various buses to achieve the aforementioned post-penalty objectives. The proposed methodology is compared with sequential learning and optimization (SLO), which trains the accuracy of load and PTDF predictions rather than economic operation. The experimental results demonstrate the superiority of ILO in improving economic operation in a noticeable way by minimizing ex post penalties and line overload in the electricity market.