What is the rule/theorem/inequality that can be applied to this integral:
$$ \int_a^b {d^k \over dt^k}x(t)e^{-j2\pi ft}\,df $$ so that I can write this inequality ?
$$ \left\lvert\int_a^b {d^k \over dt^k}x(t)e^{-j2\pi ft}\,df\right\rvert\leq\int_a^b \left | {d^k \over dt^k}x(t)\right | dt $$
I found this inequality (I don't know if it has a specific name):
$$ \left\lvert\int_a^b f(x)\,dx\right\rvert\leq\int_a^b\lvert f(x)\rvert dx $$
However this doesn't explain to me the switch from $dt$ to $df$ in the right member of the inequality.
NOTE: The $j$ in the integral is instead the the equivalent of the imaginary unity $i$ for complex valued functions.