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I guess my problem is related to this one:

var('Nr N1 N2 yr x1 x2 y2 Pr p0 P1 p2')
assume(N1>0, N2>0, Nr>0, Pr>0, p0>0, p2>0, p0+p2-1<0);
assume(P1-Nr*p2+p2-Nr*p0+p0+Nr-1>0)
h1 = 1/sqrt(2*pi*Nr)*exp(-(yr-(x1+x2))^2/(2*Nr))/sqrt(2*pi*N2)*exp(-(y2-sqrt(Pr/((1-p0)(Nr+P1/(1-p0-p2))))*yr)^2/(2*N2))*(y2-sqrt(Pr/((1-p0)(Nr+P1/(1-p0-p2))))*yr)/Nr*sqrt(Pr/((1-p0)*(Nr+P1/(1-p0-p2))))*yr*(1/(2*(1-p0))-P1/(2*(1-p0-p2)^2*(P1/(1-p0-p2)+Nr)))+1/sqrt(2*pi*N2)*exp(-(y2-sqrt(Pr/((1-p0)(Nr+P1/(1-p0-p2))))*yr)^2/(2*N2))/sqrt(2*pi*Nr)*exp(-(yr-(x1+x2))^2/(2*Nr))*(yr-(x1+x2))/Nr*x1^3/(2*P1); h1
h2 = 1/2*h1(x2=0,x1=sqrt(P1/(1-p0-p2)))+1/2*h1(x2=0,x1=-sqrt(P1/(1-p0-p2))); h2
py2x1x2 = integrate(h2,yr,-oo,oo); py2x1x2
Traceback (click to the left of this block for traceback)
...
Is  p2+p0-1  positive or negative?

The important parts are

assume(p0+p2-1<0);

and

Is  p2+p0-1  positive or negative?

obviously. Did I get you right, this is not supposed to work?

Thank you