I wonder how to obtain the second equality as follows in Eq. (44) of 

> Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. M Bukov, L D'Alessio & A Polkovnikov. [*Adv. Phys.* **64**, 139 (2015)](http://dx.doi.org/10.1080/00018732.2015.1055918), [arXiv:1407.4803](https://arxiv.org/abs/1407.4803).

which reads

\begin{eqnarray}
K_\mathrm{eff}^{(1)}[t_0](t)&=&\frac{1}{\hbar}\int_{t_0}^t dt'(H(t')-H_F^{(1)}[t_0]) \nonumber \\
&=& -\frac{1}{2\hbar} \left[\int_{t}^{t+T} dt'H(t') \left(1+2\frac{t-t'}{T} \right)-\int_{t_0}^{t_0+T} dt'H(t') \left(1+2\frac{t_0-t'}{T} \right) \right]
.
\end{eqnarray}