  We investigate first and second order fluctuations of additive functionals of
a fractional Brownian motion (fBm) of the form
\begin{align}\label{eq:abstractmain}
Z_n=\left\{\int_{0}^{t}f(n^{H}(B_{s}-\lambda))ds\ ; t\geq 0 \right\}
\end{align} where $B=\{B_{t}; t \geq 0\}$ is a fBm with Hurst parameter $H\in
(0,1)$, $f$ is a suitable test function and $\lambda\in \mathbb{R}$. We develop
our study by distinguishing two regimes which exhibit different behaviors. When
$H\in(0,1/3)$, we show that a suitable renormalization of $Z_n$, compensated by
a multiple of the local time of $B$, converges towards a constant multiple of
the derivative of the local time of $B$. In contrast, in the case $H\in[1/3,1)$
we show that $Z_n$ converges towards an independent Brownian motion
subordinated to the local time of $B$. Our results refine and complement those
from the current literature and solve at the same time the critical case
$H=1/3$, which had remained open until now.
