In Hotta, Takeuchi, Tanisaki's book on "D-modules, Perverse Sheaves, and Representation theory", for a morphism of smooth algebraic varieties $f:X \to Y$, they use the notation
$$
\int_f:D^b(D_X^{op}) \to D^b(D_Y^{op})
$$
for the derived pushforward of right $D$-modules. What motivates this notation with the integral?