Volumes of solid with known cross-sections

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  1. A solid has a base bounded by y=x2+1y=- {x\over2}+1, x=2x=-2,and x=1x=1. If the parallel cross-sections perpendicular to the base are squares, find the volume of this solid.
    1. A solid has a base bounded by these two curves, y= sin x, y= cos x. If the parallel cross-sections perpendicular to the base are equilateral triangles, find the volume of this solid.