This paper focuses on the further improved stability criteria of uncertain T-S fuzzy systems with time-varying delay by the delay-partitioning approach and a new integral inequality, i.e., the Free-Matrix-Based integral inequality. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then, new results on tighter bounding inequalities such as Peng-Park's integral inequality (reciprocally convex approach) and the Free-Matrix-based integral inequality (which yields less conservative stability criteria than the Wirtinger-based inequality) are introduced to reduce the enlargement in bounding the derivative of LKF as much as possible, therefore, less conservative results can be expected in terms of e_s and MIs. Finally, a numerical example is included to show that the proposed conditions are less conservative than existing ones.