You are not doing anything wrong. "int" just is not able to compute a closed form of the integral in this case. It is possible a closed form does not exist. To approximate the definite integral numerically, the documentation page suggests using "vpa":
Also, if you create the integration object and then later have numeric values to plug in for the variables, you can substitute in those numeric values and the integration object will update. As you fill in values for the variables the integration should become closed form. For example, if you start with the following definitions:
>> syms a b c d E f g x y;
>> func(x,y) = a+f*x+g*y*d*(y-c)/((y-c)^2+(x-b)^2)^(1/2);
>> integr = int(func(x,E),x,-E,E)
integr =
int(a + f*x + (E*d*g*(E - c))/((E - c)^2 + (b - x)^2)^(1/2), x, -E, E)
and then update "b" to be 2
>> integr = subs(integr, b, sym(2))
integr =
int(a + f*x + (E*d*g*(E - c))/((x - 2)^2 + (E - c)^2)^(1/2), x, -E, E)
and "c" to be 3
>> integr = subs(integr, c, sym(3))
integr =
2*E*a - 3*E*d*g*(asinh((E - 2)/((E - 3)^2)^(1/2)) + asinh((E + 2)/((E - 3)^2)^(1/2))) + E^2*d*g*(asinh((E - 2)/((E - 3)^2)^(1/2)) + asinh((E + 2)/((E - 3)^2)^(1/2)))
"integr" now is in closed form.
