How to integrate a squared derivative for the swing equation? While going to some literature of Power System Stability for generators I came across a derivation of the power angle when a fault occurs from the swift equation.
The Swing Equation is:
$\mathbf{\frac {2H}{w_s}}\frac{d^2\delta}{dt^2}=P_m-P_e $
Where: 
$ H$ is the inertia constant, $w_s = 2{\pi}f$, $\delta$ = power angle and $P_m$ and $P_e$ are the mechanical and electrical power, respectively, and $P_e$ becomes zero at the fault moment.
From here is where I don't understand the maths that go behind to solve for the power angle $\delta_1$.
After a first integration the literature says to give :
$\mathbf{\frac {2H}{w_s}}\frac{d\delta}{dt}=P_mt+constant $ 
I don't understand how the $\int{\frac{d^2\delta}{dt^2}}dt$ was integrated to give $\frac{d\delta}{dt}$. Which property is this?
And finally after a second derivation it gives: 
$\mathbf{\frac {2H}{w_s}}\delta= \frac{1}{2}P_mt^2+constant $
Which after solving for delta yields:
$\delta_1= \frac{w_s}{4H}(P_mt^2)+ \delta_0$
Once again, how do you integrate $\int{\frac{d\delta}{dt}}dt$
I would appreciate if someone could walk me through the process or if I'm missing something.

hint
the antiderivative of the derivative of a function $f $ if $f $. this is the first FOUNDAMENTAL THEOREM OF INTEGRAL CALCULUS.
$$\int f'=f $$
under some conditions.
$\frac {d\delta}{dt} $ is the derivative of $\delta $.
