Could we approximate $\int_0^1\frac{1}{x^4}dx$ using a Riemann sum?

We know that in 1 dimension, the integral $\int_0^1\frac{1}{x^4}dx$ is not finite. But could we approximate this integral using a Riemann sum?

In particular, if we divide the interval $[0,1]$ into equal-length partitions $0=x_0\leq x_1\leq \dots \leq x_n=1,$ with $\Delta_i=|x_{i}-x_{i-1}|=\frac{1}{n}$ for all $1\leq i\leq n,$ do we have $\sum_{i=1}^n \Delta_if(x_{i})$ converge to $\int_{1/n}^{1} \frac{1}{x^4}dx$ as $n\to \infty?$

Could we give a bound on the difference

$$\big|\int_{1/n}^1 \frac{1}{x^4}dx-\sum_{k=1}^{n}\frac{1}{(\frac{k}{n})^4}\frac{1}{n}\big|$$to get the rate of convergence of the Riemann sum as $n\to \infty?$

Thank you very much for any of your helps or useful references!