Evaluating Limit of Sum Using Integration

Question

I am trying to evaluate the following: $\lim_{n\to\infty} \sum_{j=1}^{n-1} \frac{1}{\sqrt{j(n-j)}}$ by first expressing the quantity as an integral and then evaluating the integral. The problem I'm having is expressing this as an integral. When trying to re-write the expression inside of the summation into something of the form $f(x_i)*\Delta x$, I am running into issues. I have tried factoring out an $n$ from the denominator, as well as different re-arrangements.