Quick question about finite area / infinite area

Here's a question I have...

Let S be the region between the graphs $\displaystyle y = \frac {1}{x}$ and $\displaystyle y = \frac {1}{\sqrt {x}}$ between x = 0 and x = 1. Does S have finite area? Justify your answer.

Now, so do I first do this... $\displaystyle \int_{0}^{1} \frac{1}{x}$ and I figured out that this ends up diverging to $\displaystyle \infty$. So does this mean that S has an infinite amount of area? Please tell me if I'm doing this correctly. Thanks.