# Need help understanding where this formula is derived from

I was reading the book interesting integrals and this came up: $$\int_{j}^{j+1} \frac{n-j}{x} \mathrm{d}x$$ it then goes on to say that $j$ is equal to floor $x$ because the integration interval $j \leq x < j+1$. I get this but aren't the limits of integration on the interval $j\leq x\leq j+1$?