In this paper, we consider the cellular Internet of unmanned aerial vehicles (UAVs), where UAVs sense data for multiple tasks and transmit the data to the base station (BS). To quantify the 'freshness' of the data at the BS, we bring in the concept of the age of information (AoI). The AoI is determined by the time for UAV sensing and that for UAV transmission, and gives rise to a trade-off within a given period. To minimize the AoI, we formulate a joint sensing time, transmission time, UAV trajectory, and task scheduling optimization problem. To solve this problem, we first propose an iterative algorithm to optimize the sensing time, transmission time, and UAV trajectory for completing a specific task. Afterwards, we design the order in which the UAV performs data updates for multiple sensing tasks. The convergence and complexity of the proposed algorithm, together with the trade-off between UAV sensing and UAV transmission, are analyzed. Simulation results verify the effectiveness of our proposed algorithm.