Help me understand the meaning of these lines

[navneet9431]

What does the author want to say through these lines?
What is the *harm* he is talking about?

I will be thankful for any help!

 

[PeroK]

It's a strange way to describe things. The calculation involving a finite $dx$ is an approximation. You effectively take the mass element from $x$ to $x + dx$ all to be at position $x$. As $dx$ gets smaller, the approximation gets better. The limit $dx \rightarrow 0$ is the integral.