With the rapid expansion of the Internet of Things (IoT), sensors, smartphones, and wearables have become integral to daily life, powering smart applications in home automation, healthcare, and intelligent transportation. However, these advancements face significant challenges due to latency and bandwidth constraints imposed by traditional cloud based machine learning (ML) frameworks. The need for innovative solutions is evident as cloud computing struggles with increased latency and network congestion. Previous attempts to offload parts of the ML pipeline to edge and cloud layers have yet to fully resolve these issues, often worsening system response times and network congestion due to the computational limitations of edge devices. In response to these challenges, this study introduces the InTec (Integrated Things Edge Computing) framework, a groundbreaking innovation in IoT architecture. Unlike existing methods, InTec fully leverages the potential of a three tier architecture by strategically distributing ML tasks across the Things, Edge, and Cloud layers. This comprehensive approach enables real time data processing at the point of data generation, significantly reducing latency, optimizing network traffic, and enhancing system reliability. InTec effectiveness is validated through empirical evaluation using the MHEALTH dataset for human motion detection in smart homes, demonstrating notable improvements in key metrics: an 81.56 percent reduction in response time, a 10.92 percent decrease in network traffic, a 9.82 percent improvement in throughput, a 21.86 percent reduction in edge energy consumption, and a 25.83 percent reduction in cloud energy consumption. These advancements establish InTec as a new benchmark for scalable, responsive, and energy efficient IoT applications, demonstrating its potential to revolutionize how the ML pipeline is integrated into Edge AI (EI) systems.