  In this paper we provide two-sided attainable bounds of Jensen type for the
generalized Sugeno integral of {\it any} measurable function. The results
extend the previous results of Rom\'an-Flores et al. for increasing functions
and Abbaszadeh et al. for convex and concave functions. We also give
corrections of some results of Abbaszadeh et al. As a by-product, we obtain
sharp inequalities for symmetric integral of Grabisch. To the best of our
knowledge, the results in the real-valued functions context are presented for
the first time here.
