Find f'(0.5) for f(x)=f on the top "x" on the bottom "0" Arc tan(t)dt

Answer 1

Or, more conventionally (I think)
f(x) = ∫[0,x] arctan(t) dt
By the 2nd FTC,
f'(x) = arctan(x)
so,
f'(0.5) = arctan(0.5) ≈ 0.46