Artificial Intelligence/Machine Learning (AI/ML) methods for network automation have been widely adopted by the standardization community since 5G, due to its capability to learn patterns from continuously changing network data. Presently, AI in the current 3GPP releases is specified to be deployed as an overlay or add-on feature on top of conventional Network Functions (NFs), emitting a few limitations. First, NFs need to consult the AI-overlay to derive and execute intelligent actions, thereby affecting system and AI performance and lacking intelligent autonomy. Second, the capability of NFs and NF instances to added or removed based on changing network conditions is severely hindered, resulting in limited flexibility of NF deployment. To mitigate these limitations, this article explores standard enablers for evolution from AI-overlay in 5G to native AI in 6G, where AI will be an embedded functionality of 6G-NFs. Via envisioned standards enablers-AI/ML Data Plane and Control Plane-we conceive an Integrated Distributed AI Automation Layer (INTDAI), where each 6G-NF is equipped with the capabilities of an Intelligent Agent (IA)-independent data collection, intelligent decision-making and independent action execution. A special 6G-NF, the AI Controller, controls and manages a group of IAs to ensure overall system performance. The behavior and benefits of INTDAI are illustrated using a dedicated network automation use case, Dynamic User Plane Task Migration. By means of numerical analysis, we demonstrate the gain of INTDAI, motivating the need for future standardization work for AI-native 6G.