Divide a function into intervals such way that the figures under the graph on each interval have centers of mass in integers

Question

Can we divide the real line into intervals $(a_i,b_i)$ such a way that for a given function $f(x)$ the figure under its graphic on each interval had center of mass in an integer?

The formula for center of mass is

$$x_i=\frac{\int_{a_i}^{b_i} x f(x) dx}{\int_{a_i}^{b_i} f(x) dx}$$

So we should find such $a_i, b_i$ that for each pair, the above expressed $x_i$ was an integer.

Is there a simple way?