If I understand your question you have
and you want to find the Riemann Sum approximation of
With $n=4$ It should be pretty clear that your left endpoints will be $-2, -1, 0, 1$, and that $\Delta x=1$
This matches with what you found.
So your Riemann sum is
$f(-2)+f(-1)+f(0)+f(1) = 4+0-2-2=0$
how you got 60 out of this I don't know.
The actual definite integral above is equal to $-\dfrac 8 3$.
The Riemann Sum is just an approximation. If you let n=8 you find the Riemann Sum equals $-\dfrac 3 2$, i.e.
the approximation improves with increasing $n$ as is expected.