It looks sound to me.
Find K so that
integral of f(t)dt from [-1,x] + K = integral of f(t)dt from [3,x]
WORK
K = integral of f(t)dt from [3,x] - f(t)dt from [-1,x]
K = integral of f(t)dt from [3,x] + f(t)dt from [x,-1]
K = integral of f(t)dt from [3,-1]
Anti-derivative = 4x-(3/2)x^2
4x-(3/2)x^2 from [3,-1]
= -4
Let me know if my work is sound.