Find f if f''(x)=2+cos(x)

Question

f(0)=5
f(pi/2)=−3

Answer 1

f"(x) = 2+cos(x)
f'(x) = 2x + sin(x) + c1
f(x) = x^2 - cos(x) + c1*x + c2
f(0) = -1+c2 = 5 --> c1=6
f(π/2) = π^2/4 + c1*π/2 + 6 = -3

f(x) = x^2 - cos(x) + (π/2 - 18/π)x + 6