Verified answer

а) f(x)=x³; F(-1)=2 => x=(-1), y=2

F(x) = ∫x³ dx = x⁴/4 + C

(-1)⁴/4 + C = 2

C = 2 - 1/4

C = 1,75

F(x) = x⁴/4 + 1,75

б) f(x)=sin x, F(π/3)=1 => x=π/3, y=1

F(x) = ∫sin x dx = -cos x + C

- cos(π/3) + C = 1

C = 1 + 1/2

C = 1,5

F(x) = 1,5 - cos x