We know that from the existence theorem of primitive function, if the function f(x) is continuous in a certain interval, then there is an primitive function whose derivative function f(x) is F(x). The function [x] 4 is continuous only when the interval [k, k+ 1) k is an integer, so it must be integrated by segments. The indefinite integral on [k, k+ 1] is (1/5) x 5+c, and k is an integer.