Improper integral/Independence of starting point/Exercise

Let ${}I$ be an interval, ${}r$ a boundary point of ${}I$ and

$f\colon I\longrightarrow \mathbb {R}$

a continuous function. Prove that the existence of the improper integral

$\int _{a}^{r}f(t)dt$

does not depend on the choice of the starting point ${}a\in I$.

Create a solution