F'(x) = x^3+3x^-3 F(1)= -11/20 Integral f(x) dx = ?

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f(x) = ∫f'(x) dx
f(x)= ∫ (x³ + 3 x⁻³) dx = 1/4 x⁴ - 3/2  x⁻² + c
f(1) = -11/20
1/4(1)⁴ - 3/2 (1)⁻² + c = -11/20
1/4 - 3/2 + c = - 11/20
5 - 30 + 20 c = -11
-25 + 20 c = -11
20 c = -11 + 25
20 c = 14
c = 14/20
c= 7/10
f(x) = 1/4 x⁴ - 3/2 x⁻² + 7/10

∫ f(x) dx = ∫ (1/4 x⁴ - 3/2 x⁻² + 7/10) dx
= 1/20 x⁵ + 3/2 x⁻¹ + 7/10 x + c
= 1/20  x⁵ + 3/(2x)  + 7/10  x + c