Yes, that's correct

The necessary and sufficient condition for the existence of Fourier series of a function $f(x)$ is the Drichlet conditions, which says that, Fourier series of a function $f(x)$ can exist only when:

1. $f(x)$ must be absolutely integrable over a period.
2. $f(x)$ must have a finite number of extrema in any given bounded interval, i.e. there must be a finite number of maxima and minima in the interval.
3. $f(x)$ must have a finite number of discontinuities in any given bounded interval, however the discontinuity cannot be infinite.

Which of the above statements is/are true?