**Introduction:**
A closed-coil helical spring is a type of spring that is formed by winding a wire in a helical shape. It is primarily used to store and release mechanical energy when subjected to a force or torque. In this case, the spring is subjected to a torque about its axis.

**Explanation:**
When a closed-coil helical spring is subjected to a torque about its axis, several types of stresses are induced in the spring wire. Let's analyze each option to determine the correct answer.

**a) Bending Stress:**
Bending stress occurs when an object is subjected to a bending moment or torque. In the case of a closed-coil helical spring, the torque applied to the spring causes it to twist, resulting in a bending stress in the wire. Therefore, option 'A' is correct.

**b) Direct Tensile Stress of Uniform Intensity at its Cross-Section:**
Direct tensile stress occurs when an object is subjected to a pulling force that tends to elongate it. However, in the case of a closed-coil helical spring, the torque applied to the spring does not cause a direct tensile stress of uniform intensity at its cross-section. Therefore, option 'B' is incorrect.

**c) Direct Shear Stress:**
Direct shear stress occurs when two forces act parallel to the cross-sectional area of an object, causing it to deform by sliding one part of the material relative to another. In the case of a closed-coil helical spring, the torque applied to the spring does not cause a direct shear stress. Therefore, option 'C' is incorrect.

**d) Torsional Shearing Stress:**
Torsional shearing stress occurs when an object is subjected to a twisting or torsional force. In the case of a closed-coil helical spring, the torque applied to the spring causes it to twist, resulting in a torsional shearing stress in the wire. Therefore, option 'D' is incorrect.

**Conclusion:**
When a closed-coil helical spring is subjected to a torque about its axis, the spring wire experiences bending stress. This is because the torque applied to the spring causes it to twist, resulting in a bending stress in the wire. Therefore, the correct answer to the question is option 'A'.