The ornamental design for an icechest with integrallid seat, as shown and described.
FIG. 1 is a top perspective view of an ice chest with integral lid seat, showing my new design;
FIG. 2 is a front elevation view thereof;
FIG. 3 is a rear elevation view thereof;
FIG. 4 is a left side elevation view thereof;
FIG. 5 is a right side elevation view thereof;
FIG. 6 is a top plan view thereof; and,
FIG. 7 is a bottom plan view thereof.
The dashed broken lines shown in FIGS. 1-7 depict portions of the article that form no part of the claimed design. The dash dot lines shown in FIG. 7 represent bounds of the claimed design and form no part thereof.