Due to the advantages of flexible deployment and extensive coverage, unmanned aerial vehicles (UAVs) have great potential for sensing applications in the next generation of cellular networks, which will give rise to a cellular Internet of UAVs. In this paper, we consider a cellular Internet of UAVs, where the UAVs execute sensing tasks through cooperative sensing and transmission to minimize the age of information (AoI). However, the cooperative sensing and transmission is tightly coupled with the UAVs' trajectories, which makes the trajectory design challenging. To tackle this challenge, we propose a distributed sense-and-send protocol, where the UAVs determine the trajectories by selecting from a discrete set of tasks and a continuous set of locations for sensing and transmission. Based on this protocol, we formulate the trajectory design problem for AoI minimization and propose a compound-action actor-critic (CA2C) algorithm to solve it based on deep reinforcement learning. The CA2C algorithm can learn the optimal policies for actions involving both continuous and discrete variables and is suited for the trajectory design. {Our simulation results show that the CA2C algorithm outperforms four baseline algorithms}. Also, we show that by dividing the tasks, cooperative UAVs can achieve a lower AoI compared to non-cooperative UAVs.