When you say "obviously" --- you're mistaken. In fact, those (pretty clearly) all have area-under-the-curve close to 1.
I've drawn the same four densities, and on top of the image I've added some shapes in red (each composed only of triangles and rectangles for which the computation of area is simple) - each one has area under the red "curve" equal to 1.
Hopefully you can now see that the areas under the curves must actually be quite close to 1.
Algebraically, of course, they all demonstrably have area under the curve equal to 1.
(You may have been partly confused by the height of the pdf exceeding one, but that would only be a problem if density was probability, which it isn't.)