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FindRoot cannot find obvious solution


Here is my code in Mathematica 5:

h1=1+(y-x)^2;
h2=1+(2/3-x^2)^2;
b=h2/(h1+h2);
f=x(1-x)^2;
s=f*D[b,y];
g[y_]:=NIntegrate[s,{x,0,1}];
FindRoot[g[y]==0,{y,0.35,0.45}]

The output is

NIntegrate::inum: Integrand H is not numerical at {x} = {0.5`}.
FindRoot::cvmit: Failed to converge to the requested accuracy or precision
within 100 iteration

and it gives me y->0.45 or the upper boundary. However, when I plot g[y] I
can see that the solution is somewhere around y=0.4.  Using Solve instead of
FindRoot does not give me any solutions.

What am I doing wrong here? Thank you in advance. Mukhtar Bekkali



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