Global warming caused by excessive CO2 emissions has make it urgent to develop low-carbon economy. The carbon capture system is effective to reduce the carbon footprint of coal-fired power plants. Meanwhile, using more renewable energies such as wind power will require less generations from traditional power plants and hence limit the overall carbon emission. However, the wind power is intermittent by nature and hence may fluctuate and present a stochastic feature. In order to effectively reduce the overall carbon emission, a stochastic day-ahead scheduling optimization model with wind power integration incorporating carbon capture power plant (CCPP) and coupon-based demand response (CDR) is proposed in this work. Firstly, the formulation of CDR and the operating mechanism of CCPPs are clarified. Then the flexible operation mechanism aiming at reducing wind power curtailment and CO2 emissions is analyzed. The random forecasting errors of the day-ahead hourly wind power output and loads are considered. Monte Carlo method is applied to simulate stochastic scenarios and a scenario reduction method is applied to ease the computational burden. Simulation results with on the PJM 5-bus system and the IEEE 118-bus system demonstrate the effectiveness of the proposed method in carbon emission reduction and wind curtailments decrease.