From the example provide from the question, we know when t is not equal to 1, 2, or 3, f(t) will be t^2. In this situation, we know when t gets larger, t^2 will get larger as well. This also implicates that the area will increase with t’s increasing. f(t)=t^2 is a kind of quick increasing function, the area will also increase fast. When the area reaches a huge enough number, the area of t=1, t=2, t=3 can be ignored. Because at that time, comparing the area of f(t1), f(t2), f(t3) and other areas, the area of f(t1), f(t2), f(t3) are pretty small, these three areas will not affect whether the function is integral or not. Even in a slow growth function, as t approaches to infinity, area increased definitely. Therefore, finite points’ areas are not important any more. This is why functions with finitely many removable discontinuities are integrable.