# `f(x) = (1/2)x^2 - 2x + 6` Find the most general antiderivative of the function. (Check your answer by differentiation.)

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sciencesolve | Certified Educator

You need to evaluate the most antiderivative of the function, such that:

`int f(x) dx = F(x) + c`

`int ((1/2)x^2 - 2x + 6) dx = int(1/2)x^2 dx - int 2xdx+ int 6 dx`

`int ((1/2)x^2 - 2x + 6) dx = (1/6)x^3 - x^2 + 6x + c`

**Hence, evaluating the most antiderivative of the function yields ` F(x) = (1/6)x^3 - x^2 + 6x + c.` **