  We find a concrete integral formula for the class of generalized Toeplitz
operators $T_a$ in Bergman spaces $A^p$, $1<p<\infty$, studied in an earlier
work by the authors. The result is extended to little Hankel operators. We give
an example of an $L^2$-symbol $a$ such that $T_{|a|} $ fails to be bounded in
$A^2$, although $T_a : A^2 \to A^2$ is seen to be bounded by using the
generalized definition. We also confirm that the generalized definition
coincides with the classical one whenever the latter makes sense.
