Artificial Intelligence(AI) is an emerging technology that finds its application in various industries. Integration of AI in Unmanned Aerial Vehicles(UAVs) can lead to tremendous growth in the field of UAVs by improving flight safety and efficiency. Machine learning algorithms can enable UAVs to make real-time decisions in complex environments and reach the optimal solution that aims to fulfill a mission's requirements within the hardware constraints such as battery and payload. Several recent works in UAVs employed a variety of machine learning algorithms to enhance the capabilities of UAVs and assist them. Although several reviews have been published examining the various aspects of AI for UAVs, they are all pertaining to particular applications or technologies. Addressing this research gap, we present a comprehensive and diversified review to enable researchers to analyze the current and future requirements and develop the latest solutions utilizing AI. We have classified the reviewed works based on three different classification schemes: 1) application scenario-based, 2) AI algorithm-based, and 3) AI training paradigm-based. We have also presented a compilation of frameworks, tools, and libraries used in AI-integrated UAV systems. We identified that the integration of AI in UAVs has a wide array of applications ranging from path planning to resource allocation. We have observed that Reinforcement Learning based algorithms are more often used in AI-integrated UAV systems than other AI algorithms. Further, our findings reveal that UAV frameworks employing federated learning and other distributed machine learning paradigms are quickly emerging. Furthermore, we also have put forth several challenges and potential applications of AI-integrated UAV systems.