To simply answer the question, I believe your engine cannot make enough power in that gear to overcome the drag created at that speed. Downshifting will help, but at that point, it is just a fight between engine power and drag.

There is no speed limiter on Integras, only rev limiters. So if you have enough power to overcome the drag, you could theoretically hit the rev limiter. To go any faster, you would need a longer geared transmission.