Analog reservoir computing (ARC) systems have attracted attention owing to their efficiency in processing temporal information. However, the distinct functionalities of the system components pose challenges for hardware implementation. Herein, we report a fully integrated ARC system that leverages material versatility of the ferroelectric-to-mixed phase boundary (MPB) hafnium zirconium oxides integrated onto indium-gallium-zinc oxide thin-film transistors (TFTs). MPB-based TFTs (MPBTFTs) with nonlinear short-term memory characteristics are utilized for physical reservoirs and artificial neuron, while nonvolatile ferroelectric TFTs mimic synaptic behavior for readout networks. Furthermore, double-gate configuration of MPBTFTs enhances reservoir state differentiation and state expansion for physical reservoir and processes both excitatory and inhibitory pulses for neuronal functionality with minimal hardware burden. The seamless integration of ARC components on a single wafer executes complex real-world time-series predictions with a low normalized root mean squared error of 0.28. The material-device co-optimization proposed in this study paves the way for the development of area- and energy-efficient ARC systems.