If you can only take measurement at discrete times, then summing up and dividing by the time between measurements is the only way possible – the integral
$$E_\text{total}=\int\limits_{T_\text{start}}^{T_\text{end}} P(t) dt$$
really collapses to a sum, it \$P(t)\$ is only known for set of points. For example, assume the power value is constant for amount of time that you spend between your \$N\$ individual measurements, let's call that \$T_\text{sample}\$, then
$$\begin{align}
\tilde E &= \sum\limits_{n=0}^{N-1} T_\text{sample}\cdot P(nT)\\
&= T_\text{sample} \sum\limits_{n=0}^{N-1} P(nT)\\
\end{align}$$
Now, you say
a set of points that doesn't really have any rhyme or reason
Well, that's a problem. What if the power goes up between two measurement points, and just happens to be low every time you're actually taking note?
The answer to this problem is the Nyquist-Shannon Sampling Theorem, which is quite handy in a lot of signal processing applications, but in this case it means:
If you have a real signal (here: your power measurements) whose highest frequency is \$f_\text{max}\$, then you will need to look with twice that frequency at it to be sure not to miss anything, i.e. \$f_\text{sample}\ge 2f_\text{max}\$.
Frequency here means the amount of time between two consecutive events. That means that if you can say "the shortest power fluctuation I need to consider is \$T\$ long (e.g. 5 second)", then your signals highest frequency \$f_\text{max}= \frac1T\$ (i.e. 0.2 Hz in the 5s case), and you'll need to sample twice that often, so \$f_\text{sample} \ge 2f_\text{max}=\frac2T\$, or considering the sampling interval \$T_\text{sample}=\frac1{f_\text{sample}}\le \frac12 T\$.
If you sample slower than that, your measurement is not representative for your observed (unless you have another, restricting model for how the power consumption fluctuates, which you don't seem to have), and no statement can be drawn from your set of measurement points.
If you then have the measurements in a sensible, constant time interval, just adding them up and multiplying the result with that interval will give you your total energy reading. You don't need any special python modules for that, i.e. simply
### assuming "powers" is a list / iterable of your power measurements in Watt,
### and "T" contains the sample interval in seconds
total_power = sum(powers) / 1000 * T / 3600
will give you your kWh.
Now, you might say "how should I know how fast my appliances turn on and off?"
In many scenarios, you can put a sensible limit to power fluctuation. For example, sure, lights might switch on and of within fractions of a second, but the amount of power consumed by quickly switched off lights (e.g. toilet usage, turn on, 60s, turn off) is probably negligible,
whereas things that really matter (fridge, water heater, washing machine, oven) tend to change relatively slow in a typical home usage scenario.
