The probability of a transistor failing between t a months

Question

Question: The probability of a transistor failing between t = a months and t = b months is given by

c_a∫^b e^-ct dt,

for some constant c.

(a) If the probability of failure within the first six months is 10%, what is c?

(b) Given the value of c in part (a), what is the probability the transistor fails within the second six months?