To find the area bounded by the curves, we need to find the points of intersection between the two curves.

Setting y = |x| - 1 and y = - |x| + 1 equal to each other, we get:

|x| - 1 = - |x| + 1

Adding |x| to both sides:

2|x| - 1 = 1

Adding 1 to both sides:

2|x| = 2

Dividing both sides by 2:

|x| = 1

Taking the positive and negative values of x, we get x = 1 and x = -1.

Now we can find the area between these two points by integrating the absolute difference between the two curves.

The integral of the absolute difference between the two curves from x = -1 to x = 1 is:

∫ [(|x| - 1) - (-|x| + 1)] dx

Simplifying the expression inside the integral:

∫ [2|x| - 2] dx

Splitting the integral into two parts:

∫ 2|x| dx - ∫ 2 dx

Integrating each part:

2 ∫ |x| dx - 2 ∫ dx

For the first integral, we can split it into two cases:

When x is positive, |x| = x:

2 ∫ x dx - 2 ∫ dx

Integrating:

x^2 - 2x + C

When x is negative, |x| = -x:

2 ∫ -x dx - 2 ∫ dx

Integrating:

- x^2 - 2x + C

Now we can find the definite integral from x = -1 to x = 1:

[x^2 - 2x] from -1 to 1 + [-x^2 - 2x] from -1 to 1

[(1)^2 - 2(1)] - [(-1)^2 - 2(-1)] + [-(1)^2 - 2(1)] - [(-1)^2 - 2(-1)]

[1 - 2] - [1 + 2] + [-1 - 2] - [1 + 2]

-1 - 3 - 3 - 3

-10

Therefore, the area bounded by the curves y = |x| - 1 and y = - |x| + 1 is -10.

Since the area cannot be negative, the answer is none of the given options (a) 1, b) 2, c) 2).