If I try:

    RegionPlot[{y > x - 1 && y^2 < 2 x + 6}, {x, -4, 6}, {y, -3, 5},
     Mesh -> None]

I get:

[![enter image description here][1]][1]

However, if I combine it with a ContourPlot:

    Show[
     ContourPlot[{y == x - 1, y^2 == 2 x + 6}, {x, -4, 6}, {y, -3, 5},
      Axes -> True, AxesLabel -> Automatic,
      PlotLegends -> "Expressions"],
     RegionPlot[{y > x - 1 && y^2 < 2 x + 6}, {x, -4, 6}, {y, -3, 5},
      Mesh -> None]
     ]

I get this:

[![enter image description here][2]][2]

Is there any way to get rid of all the mesh-like segments in the image? I did try Mesh->None.


  [1]: https://i.stack.imgur.com/Fk8mg.png
  [2]: https://i.stack.imgur.com/2AjqK.png