Ответ: 1 - π/4

Объяснение: ∫₀¹x²dx/(x²+1) = ∫₀¹(x²+1-1)dx/(x²+1) =∫₀¹(x²+1)dx/(x²+1) -∫₀¹dx/(x²+1) =∫₀¹dx - ∫₀¹dx/(x²+1) = x|₀¹ - arctg(x)|₈¹= (1-0) -  (arctg1-arctg0)= 1-(π/4- 0)= 1-π/4