# What is #f(x) = int -x^2+x-4 dx# if #f(2) = -3 #?

To find c, the constant of integration, substitute x = 2 , y = - 3

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To find ( f(x) ), we need to find the antiderivative of ( -x^2 + x - 4 ), which is ( -\frac{1}{3}x^3 + \frac{1}{2}x^2 - 4x + C ), where ( C ) is the constant of integration.

Since ( f(2) = -3 ), we can use this information to solve for ( C ): [ f(2) = -\frac{1}{3}(2)^3 + \frac{1}{2}(2)^2 - 4(2) + C = -3 ] [ -\frac{8}{3} + 2 - 8 + C = -3 ] [ C = -3 + \frac{8}{3} - 2 + 8 ] [ C = \frac{1}{3} ]

Therefore, ( f(x) = -\frac{1}{3}x^3 + \frac{1}{2}x^2 - 4x + \frac{1}{3} ).

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