If f is a bounded function from [a,b] into the real numbers that is

integrable on [a,b], then for any c such that a < c < b, is f

integrable on [a,c] and is f integrable on [c,b]?

I want to say no, since if I pick $\displaystyle f(x)= \frac {1}{x} $, then f is integrable from [-2,2] but not if you move the boundary to 0.

Is that right? Thanks.