題組內容

3. Let $f(x) = \frac{1}{1 + x^2}$, $0 \leq x \leq 1$ and $P = \{0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1\}$ be a partition of $[0, 1]$.

(a) \( (7\%) \) Calculate the upper sum \( U(f,p) \) and the lower sum \( L(f,p) \) of \( f \) over the partition \( P \). Rounded the answers to the third decimal place.