$f(x) / p_1 (x)$ tends to change a lot less whereas $f(x) / p_2 (x)$ varies a lot more (very big for small $x$ and very small for big $x$), so when doing the Monte Carlo estimate where you sum up $f(X_i) / p(X_i)$, the variance of each individual sample will be significantly higher, so the variance of the estimator will be lower if we sample from $p_1$ instead of $p_2$. This seems to indicate that the "ideal" PDF would just be $f(x)$ normalized to have unit area.