Let `f(x)=int_0^x e^t.sin(x-t) dt and g(x)=f(x)+f''(x).` Which of the following statements are correct ?

Let f(x) be a derivable function satisfying f(x)=int_0^x e^t sin(x-t) dt and g(x)=f '' (x)-f(x) Then the possible integers in the range of g(x) is_______

Let f(x) be a derivable function satisfying f(x)=int_0^x e^tsin(x-t)dt and g(x)=f''(x)-f(x) Then the possible integers in the range of g(x) is_______

Let f(x) be a derivable function satisfying f(x)=int_(0)^(x)e^(t)sin(x-t)dt and g(x)=f'(x)-f(x) Then the possible integers in the range of g(x) is

If f(x) = int_(0)^(x) t sin t dt, then f'(x) is

Let f(x)=int_(0)^(1)|x-t|dt, then

Let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true?