The correct influence line for bending moment at point C can be determined by considering the characteristics of the beam and the loading conditions.

To determine the influence line for bending moment at point C, we need to consider the effect of a unit load placed at different positions along the length of the beam.

The given figure shows a simply supported beam with a point load P at point B. The beam has a length L and supports at points A and D. Point C is located at a distance x from point A.

To determine the influence line for bending moment at point C, we need to consider the effect of a unit load placed at different positions along the length of the beam.

We can divide the beam into two parts: AB and BC.

1. Influence Line for AB:
In this case, the unit load is placed at point B. When the unit load is at point B, the beam will be subjected to a positive bending moment at point C. As the unit load moves from B towards point A, the bending moment at point C decreases linearly. Therefore, the influence line for bending moment at point C in the AB section is a downward sloping straight line.

2. Influence Line for BC:
In this case, the unit load is placed at point C. When the unit load is at point C, the beam will be subjected to a negative bending moment at point C. As the unit load moves from C towards point D, the bending moment at point C increases linearly. Therefore, the influence line for bending moment at point C in the BC section is an upward sloping straight line.

To obtain the overall influence line for bending moment at point C, we need to combine the influence lines for AB and BC. Since the influence lines are linear, we can simply superimpose them.

- The overall influence line for bending moment at point C is a downward sloping straight line from A to B and an upward sloping straight line from B to D.