How to 1d intergrate along x/y direction in 2d mesh

General Discussion
4

This is a other story,

One idea : use the levelest integral

load "msh3"
mesh Th=square(10,10);
meshL Lyh=segment(10,[0,x,0]);
fespace Vh(Th,P1);
fespace Lh(Lyh,P1);
Vh u =y+x; // 
Lh yy=y; 
Lh  v ;
for [i,vi:v[]]  {
	vi = int1d(Th,levelset=y-yy[][i])(u); // integral on y = yy[][i] of u ..
}
cout << v[] << endl;

remark, we miss the last line y= 1 due to roundoff error.