We study the exponential synchronization of coupled inertial neural networks with both discrete-time delay and distributed delay by quantized pinning controllers. Novel integral inequalities, which generalize the Jensen-based inequality, are developed by choosing appropriate weight functions in our recent work. An exponential synchronization criterion is established by applying these inequalities to analyzing a Lyapunov-Krasovskii functional which takes mixed delays into account. Numerical simulations show that the criterion can reduce conservativeness when designing parameters of the controller.