What is $\int_1^\infty du/u - \int_1^\infty du/u$?

Question

I thought that $\int_1^\infty \frac{du}{u}- \int_1^\infty \frac{du}{u} = 0$ as the two integrals are the same or because we can write it as $\int_1^\infty \left(\frac{1}{u} - \frac{1}{u}\right)du$, but my teacher told me that $\int_1^\infty \frac{du}{u}- \int_1^\infty \frac{du}{u}$ is an indeterminate form. Is my logic wrong? If it is wrong, how can i show formally that $\int_1^\infty \frac{du}{u}- \int_1^\infty \frac{du}{u} = 0$?