Find the area between the curves.
\[
x=-2, x=1, y=x, y=x^{2}-2
\]

The area between the curves is $\square$.
(Type an integer or an improper fraction. Simplify your answer.)

Step 1 ：We are given the curves \(x=-2\), \(x=1\), \(y=x\), and \(y=x^{2}-2\). We are asked to find the area between these curves.

Step 2 ：We can find the area between the curves by subtracting the lower function from the upper function and integrating from the leftmost to the rightmost x-values. In this case, the upper function is \(y=x\) and the lower function is \(y=x^{2}-2\). The leftmost x-value is -2 and the rightmost x-value is 1.

Step 3 ：Subtracting the lower function from the upper function gives us \(f = x - (x^{2} - 2)\), which simplifies to \(f = -x^{2} + x + 2\).

Step 4 ：We integrate this function from -2 to 1 to find the area between the curves. The integral of \(f\) from -2 to 1 is \(\frac{3}{2}\).

Step 5 ：Final Answer: The area between the curves is \(\boxed{\frac{3}{2}}\).