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To address the challenge of global warming stemming from excessive fossil fuel combustion, the exploration of low-carbon technologies and improvements to carbon trading mechanisms stand out as vital strategies. An effective conduit for these strategies is the integrated energy system (IES), which has garnered increasing attention for its potential. To realize low-carbon advancements within energy systems, this study proposes a low-carbon economic scheduling framework for the IES that integrates the coupled operation of carbon-capture power plants, power-to-gas (CCPP–P2G) unit and the price-based demand response (PDR) considering dynamic carbon trading mechanisms. The proposed approach firstly concurrently considers source-side CCPP-P2G and load-side PDR to achieve coordinated low-carbon operation, elucidating the underlying mechanisms. Subsequently, a dynamic carbon trading model for the IES is formulated, flexibly capturing the ebb and flow of supply and demand in the carbon trading market. Amidst the uncertainty of the system, a bi-level optimization model is constructed to minimize the operational cost. Finally the effectiveness of the proposed method is demonstrated on an IES consisting of the IEEE-30 bus power system, 6-bus natural gas system and 6-bus district heating system. The findings indicate that the proposed dynamic carbon trading mechanism is able to effectively provide time-varying carbon trading price signals to fully reflect the supply and demand relationship of carbon emission allowance. Furthermore, the synchronized operation of CCPP-P2G and PDR yields substantial benefits, compared to the benchmark. Specifically for the test case, the proposed framework reduces system operational costs, wind power curtailment, and carbon emissions by $87,160, 1,410 MWh, and 4,849t, respectively. [ABSTRACT FROM AUTHOR]