Function handle: intergal of another integral

Good morning everyone, I'm trying to solve a quadruple integral with the function handle. The problem is that between them there is a double integral on a domain R. so I decided to first solve the integrals on the domain R and then integrate the result with respect to the other two variables but I have some trouble.

I know that I could solve symbolically but the "intpoly" function only works with "function handle";

my code is:

mi=[1:2:100]' %where mi, xi, yi are arrays with same length.
xi=[1:3:150]'
yi=[1:4:200]'
B=1.09*log(10) %costant value 
fun=@(t,m,x,y) ((B./(t-1943)).*exp(-B.*(m-5.75))).*sum((mi(1:50)-5.75).*(1/pi).*(1./(((x-(xi(1:50)).^2+(y-yi(1:50).^2))))))  
t1=1965
t2=2000
m1=5.75
m2=8
G=@(T,M,X,Y) arrayfun(fun,T,M,X,Y)
 F=integralN(G,t1,t2,m1,m2,174,180,-35,-41)  %if I solve the integralN (not considering the polygon R) there are no mistakes 
F2=integral2(@(T,M) intpoly(@(X,Y) G(T,M,X,Y), [177.63,182.17,178.7,175.55,177.63],[-37,-37,-40.87,-39.3,-37]),t1,t2,m1,m2)
%if i solve this last matlab gives me the sequent errors:

Error using arrayfun
All of the input arguments must be of the same size and shape.
Previous inputs had size 14 in dimension 1. Input #4 has size 2

Error in INTEGRALE_SUL_DOMINIO>@(T,M,X,Y)arrayfun(fun,T,M,X,Y)

Error in INTEGRALE_SUL_DOMINIO>@(X,Y)G(T,M,X,Y)

Error in integral2Calc>integral2t/tensor (line 237)
            Z1 = FUN(X(VTSTIDX),Y(VTSTIDX)); NFE = NFE + 1;

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 106)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

Error in intpoly (line 40)
z=integral2(f,xmin,xmax,ymin,ymax);

Error in
INTEGRALE_SUL_DOMINIO>@(T,M)intpoly(@(X,Y)G(T,M,X,Y),[177.63,182.17,178.7,175.55,177.63],[-37,-37,-40.87,-39.3,-37])

Error in integral2Calc>integral2t/tensor (line 228)
        Z = FUN(X,Y);  NFE = NFE + 1;

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 106)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

Error in INTEGRALE_SUL_DOMINIO (line 13)
F2=integral2(@(T,M) intpoly(@(X,Y) G(T,M,X,Y), [177.63,182.17,178.7,175.55,177.63],[-37,-37,-40.87,-39.3,-37]),t1,t2,m1,m2)
 
>>Thanks for your help!