Decision-making often requires the accumulation and maintenance of evidence over time. Although the neural signals underlying sensory processing have been studied extensively, little is known about how the brain accrues and holds these sensory signals to guide later actions. Previous work has suggested that neural activity in the lateral intraparietal area (LIP) of the monkey brain reflects the formation of perceptual decisions in a random dot direction-discrimination task in which monkeys communicate their decisions with eye-movement responses. We tested the hypothesis that decision-related neural activity in LIP represents the time integral of the momentary motion "evidence." By briefly perturbing the strength of the visual motion stimulus during the formation of perceptual decisions, we tested whether this LIP activity reflected a persistent, integrated "memory" of these brief sensory events. We found that the responses of LIP neurons reflected substantial temporal integration. Brief pulses had persistent effects on both the monkeys' choices and the responses of neurons in LIP, lasting up to 800 ms after appearance. These results demonstrate that LIP is involved in neural time integration underlying the accumulation of evidence in this task. Additional analyses suggest that decision-related LIP responses, as well as behavioral choices and reaction times, can be explained by near-perfect time integration that stops when a criterion amount of evidence has been accumulated. Temporal integration may be a fundamental computation underlying higher cognitive functions that are dissociated from immediate sensory inputs or motor outputs.