plotting - error with NIntegrate and RegionPlot

Bug introduced in 10.2 or earlier and persisting through 11.0.1 or later

Here's a simplified example of what I'm trying to do:

RegionPlot[
  NIntegrate[PDF[NormalDistribution[0, 1], a], {a, 0, y}] >= 0.2,
                {x, -1, 1}, {y, 0.1, 0.7}]

(yes, it doesn't depend on x)

This returns an inscrutable error:

Throw::nocatch: "Uncaught \!\(Throw[\(-Holonomic`DifferentialRootReduceDump`y[NIntegrate`LevinRuleDump`x]\)
+ \*SuperscriptBox[\"Holonomic`DifferentialRootReduceDump`y\", \"\[Prime]\",

MultilineFunction->None][NIntegrate`LevinRuleDump`x],
NIntegrate`LevinRuleDump`FastLookupHolonomicDifferentialEquation]\) returned to top level."

I'm using Mathematica 10.2. Any ideas what's wrong?

EDIT: I'm not looking for algebraic simplifications or substituting Integrate for NIntegrate. The above code is just an example to reproduce the error. In the code I actually want to run, NIntegrate is the only option.

Answer

This is a bug in RegionPlot. For a possible workaround, try the following undocumented option

RegionPlot[NIntegrate[PDF[NormalDistribution[0, 1], a], {a, 0, y}] >= 0.2, 
   {x, -1, 1}, {y, 0.1, 0.7}, "NumericalFunction" -> False]

Mathematica graphics

Comments

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