Integral of 1/(sqrt(2)+sin(x))

Hi,

take a look at this:
    (C133) integrand:1/(sqrt(2)+sin(x));
    (D133) 1/(SIN(x)+SQRT(2))
    (C134) integrate(integrand,x,0,2*%pi);
    (D134) 2*%PI
    (C135) defint(integrand,x,0,2*%pi);
    (D135) 2*%PI
    (C136) ldefint(integrand,x,0,2*%pi);
    (D136) 0

Now, I have some questions:
1. Judging from the info pages I assumed that "ldefint" is more powerful
   than "defint". Then why does it return the wrong result but "integrate"
   and "defint" return the correct result?
2. Maxima returns a non continuous indefinite integral:
       (C214) ratsimp(integrate(integrand,x));
       (D214) 2*ATAN((SQRT(2)*SIN(x)+COS(x)+1)/(COS(x)+1))
   Shouldn't integrate always return a continuous function when the
   integrand is continuous?
3. Why are there both "integrate" and "defint"? According to the
   documentation they are the same. Shouldn't "defint" be flagged as
   deprecated?

Felix