Anti derivative problem please help!

f ''(x)=3x-5 and f '(-2)=-1 and f (-2)=1 find f '(x) and f (1)

Please help, thanks

f ' ' (x) = 3x - 5

f ' (x) = 3x^2 / 2 - 5x + c ... integral f ' ' (x)
. . . given f ' (- 2) = - 1
. . . -1 = 3 * (-2)^2 / 2 - 5 * (-2) + c
. . . c = - 1 - 6 - 10 = - 17

f ' (x) = 3x^2 / 2 - 5x - 17 <=====

f (x) = x^3 / 2 - 5x^2 / 2 - 17x + c ... integral f (x)
. . . given f (-2) = 1
. . . 1 = (-2)^3 / 2 - 5 * (-2)^2 / 2 - 17 * (-2) + c
. . . c = 1 + 4 + 10 - 34 = - 19

f (x) = x^3 / 2 - 5x^2 / 2 - 17x - 19 <=====

y" = 3x - 5
y' = (3/2)x² - 5x + c

-1 = 6 + 10 + c
c = -17

y' = (3/2)x² - 5x - 17
y = ½ x³ - (5/2)x² - 17x + c

1 = -4 - 10 + 34 + c
c = -19

y = ½ x³ - (5/2)x² - 17x - 19
y(1) = 1/2 - 5/2 - 17 - 19
y(1) = -38