If the derivative of a function results in 3x - 4, then finding the primitive will give your function.
[tex]\int {(3x - 4})\, dx = \frac{3x^{2}}{2} - 4x + C[/tex]
Now, when x = -1, [tex]y = \frac{13}{2}[/tex]
Thus, [tex]\frac{13}{2} = \frac{3(-1)^{2}}{2} - 4(-1) + C[/tex]
[tex]\frac{13}{2} = \frac{3}{2} + 4 + C[/tex]
[tex]\frac{13}{2} = \frac{11}{2} + C[/tex]
[tex]C = \frac{2}{2} = 1[/tex]
Thus, our primitive becomes [tex]\frac{3x^{2}}{2} - 4x + 1[/tex]
