f(x)=x+(3/2)∫[0,1]f(t)dt
f'(x)=1
f(x)=x+C ∫[0,1]f(t)dt=1/2+C
f(x)=x+3/4+C/2=x+C
C/2=3/4
C=3/2
f(x)=x+3/2