`If int_0^xf(t) dt=x+int_x^1 tf(t)dt,` then the value of `f(1)`

f(x)=int_0^x f(t) dt=x+int_x^1 tf(t)dt, then the value of f(1) is

If int_(0) ^(x) f (t) dt = x + int _(x ) ^(1) t f (t) dt, then the value of f (1) , is

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

If f(x)=int_0^x tf(t)dt+2, then

If f(x)=x+int_0^1t(x+t)f(t) dt ,then the value of 23/2f(0) is equal to _________

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

Given a function g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f '(1)+f''(1).

Given a function 'g' continous everywhere such that int _(0) ^(1) g (t ) dt =2 and g (1)=5. If f (x ) =1/2 int _(0) ^(x) (x-t) ^(2)g (t)dt, then the vlaue of f'''(1)-f''(1) is:

Given a function 'g' continous everywhere such that int _(0) ^(1) g (t ) dt =2 and g (1)=5. If f (x ) =1/2 int _(0) ^(x) (x-t) ^(2)g (t)dt, then the vlaue of f''(1)-f'(1) is: