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I agree, it must be a problem with normal. The following works as expected
sage: f(x,y)= x*y^3 sage: f (x, y) |--> x*y^3 sage: g = f.integral(y,0,7) sage: g (x, y) |--> 2401/4*x sage: plot(g,-5,5)
Where as this returns the error you've seen:
sage: f(x,y,z)= x*y^3+z
sage: g = f.integral(y,0,7)
sage: plot(g,-5,5)
...
ValueError: free variable: z
If you try to simply integrate the normal function, do you get a number, or another function of x?
