0.5 != integrate(dnorm,0,20000) = 0

I'd suggest that the original sin here is calling some particular
numerical integration routine 'integrate', which gives the user an
illusory sense of power.... Functions have to be well-behaved in
various ways for quadrature to work well, and you've got to expect
things like

integrate(function(x)tan(x),0,pi)

Error in integrate(function(x) tan(x), 0, pi) :
  roundoff error is detected in the extrapolation table   <<< a 'good'
error -- tells the user something's wrong

integrate(function(x)tan(x)^2,0,pi)

1751.054 with absolute error < 0                                  <<< oops

integrate(function(x)1/(x-pi/2)^2,0,pi)                         <<< the same pole (analytically)

Error in integrate(function(x) 1/(x - pi/2)^2, 0, pi) :         <<<
gets a useful error in this form
  non-finite function value

But by that argument, I suppose you shouldn't call floating-point
addition "+" :-)

                -s