The step of urbanization and modern civilization fosters different functional zones in a city, such as residential areas, business districts, and educational areas. In a metropolis, people commute between these functional zones every day to engage in different socioeconomic activities, e.g., working, shopping, and entertaining. In this paper, we propose a data-driven framework to discover functional zones in a city. Specifically, we introduce the concept of Latent Activity Trajectory (LAT), which captures socioeconomic activities conducted by citizens at different locations in a chronological order. Later, we segment an urban area into disjointed regions according to major roads, such as highways and urban expressways. We have developed a topic-modeling based approach to cluster the segmented regions into functional zones leveraging mobility and location semantics mined from LAT. Furthermore, we identify the intensity of each functional zone using Kernel Density Estimation. Extensive experiments are conducted with several urban scale datasets to show that the proposed framework offers a powerful ability to capture city dynamics and provides valuable calibrations to urban planners in terms of functional zones.