It is disappointing that the new FunctionDiscontinuities
does not seem to collaborate with the old Exclusions -> "Discontinuities"
:
myIndicatorFunc[a_, b_, var_] :=
Piecewise[{{0, var < a}, {1/2, var == a}, {1, a < var < b}, {1/2,
var == b}, {0, b < var}}]
FunctionDiscontinuities[myIndicatorFunc[-2, 5, y], y]
Plot[myIndicatorFunc[-2, 5, x], {x, -10, 10},
Exclusions -> "Discontinuities"]