if $ f(x)=x+\cos x $ then find $ \int_0^\pi (f^{-1}(x))\text{dx} $? I would be interest to show :
if $ f(x)=x+\cos x $  then find $ \int_0^\pi (f^{-1}(x))\text{dx} $ ?
my  second question that's make me  a problem is that :
what is :$ f^{-1}(\pi) $ ?
I would be interest for any replies or any comments .

There is something questionable in the wording (about the bounds of the integral). So, two interpretations are presented below :

