If f(x)=∫x+sin⁡xx+cos⁡xdx, then limx→∞ f(x)=

We  have       f(x)=∫x+sinxx+cosxdx⇒                     f(x)=x+sinxx+cosx⇒   limx→∞   f(x)=limx→∞1+sinxx1+cosxx=1+01+0=1      ∴limx→∞1x=0 and sinx≤1,cosx≤1 for all xHence (2) is the correct answer.