To improve automatic generation control (AGC) performance and reduce the wastage of regulation resources in interconnected grids including high-proportion renewable energy, a multi-area integrated AGC (MAI-AGC) framework is proposed to solve the coordination problem of secondary frequency regulation between different areas. In addition, a cocktail exploration multi-agent deep deterministic policy gradient (CE-MADDPG) algorithm is proposed as the framework algorithm. In this algorithm, the controller and power distributor of an area are combined into a single agent which can directly output the power generation command of different units. Moreover, the cocktail exploration strategy as well as various other techniques are introduced to improve the robustness of the framework. Through centralized training and decentralized execution, the proposed method can nonlinearly and adaptively derive the optimal coordinated control strategies for multiple agents and is verified on the two-area LFC model of southwest China and the four-area LFC model of the China Southern Grid (CSG).