How might the cold war have progressed if the u-2 incident had never occurred?

Without U-2, Eisenhower would have met with Kruschev, and they might have come to a positive resolution on the issue of Cuba. 

With Cuba resolved, Eisenhower would not have needed to launch the Bay of Pigs invasion; Castro bringing in missiles was a direct reaction to the Bay of Pigs. No Bay of Pigs, no Cuban Missile Crisis. 

Without the Cuban Missile Crisis, tensions between the US and USSR would have been reduced. Still there obviously, but reduced. It is likely Kennedy could have come to an agreement to significantly slow, if not end, the arms race with the USSR. 

And if Cuba and nuclear weapons were on a lower simmer, the US might have been less likely to stay in Vietnam. Both Yarmolinsky and McNamara had misgivings as early as 1963 about Vietnam. If the Cold War was cooler, they might have been able to keep that fire out. 

It's possible the Cold War could have taken an entirely different turn if not for one airplane being shot down.

The answer is c. hope that