First check whether (dH/dx1,dH/dx2) is conservative.
Then you can reconstruct H by using
H(x1,x2) = H(x10,x20) + integral_{z=x10}^{z=x1} dH/dx1(z,x20) dz + integral_{z=x20}^{z=x2} dH/dx2(x1,z) dz
where H(x10,x20) must be given (thus H must be fixed at a single point).
Following the example under
syms x y x1 y1
dHdx = y*cos(x) + y^2;
dHdy = sin(x)+2*x*y-2*y;
x0 = 0;
y0 = 0;
H0 = 0;
H = H0 + int(subs(dHdx,y,y0),x,x0,x1) + int(subs(dHdy,x,x1),y,y0,y1);
H = subs(H,[x1,y1],[x,y])
