To understand why the integral of an odd function from negative infinity to positive infinity is defined and finite for a bounded function, let's break down the question and explore the concepts involved.

Understanding Odd Functions:
- An odd function is a function that satisfies the property: f(-x) = -f(x) for all values of x.
- Geometrically, odd functions are symmetric about the origin (0,0) and have rotational symmetry of 180 degrees.

Defining the Integral:
- The integral of a function represents the area between the function and the x-axis over a given interval.
- When integrating over the entire real line from negative infinity to positive infinity, we are calculating the total area under the curve.

Exploring the Options:
a) Yes: The integral of an odd function from -infinity to infinity can be defined and finite for a bounded function.

b) Never: This option is incorrect because there are cases where the integral of an odd function from -infinity to infinity can be defined and finite.

c) Not always: This option is partially correct. While it is true that not all functions will have a defined and finite integral from -infinity to infinity, for a bounded odd function, the integral is defined and finite.

d) None of the mentioned: This option is incorrect because option 'a' correctly states that the integral is defined and finite for a bounded odd function.

Explanation:
- For a bounded function, the function's values are limited within a specific range, i.e., it does not tend to infinity as x approaches infinity or negative infinity.
- When integrating an odd function from -infinity to infinity, the positive and negative areas under the curve cancel each other out due to the symmetry of the function about the origin.
- As a result, the integral evaluates to a finite value, representing the net area between the function and the x-axis over the entire real line.

Conclusion:
The integral of an odd function from negative infinity to positive infinity is defined and finite for a bounded function. This is because the positive and negative areas under the curve cancel each other out due to the symmetry of the function about the origin.