5. Obviously, if a linear function is added, the condition of the problem is unchanged, and we can't expect to simply let f(b)=0 to solve the problem. In addition, pay attention to the requirement that the numerator is infinitesimal by using the 0/0 type Lobida rule, otherwise an error will occur (as long as the denominator is infinity, infinity/infinity type is an important difference). Firstly, it can be proved that the limit of(b-x) β f' (x) is zero, so the integral of f' converges in the interval [a, b], so the definition of f (b) can be supplemented.