A point mass is not an interval probability
For a binomial count with 10 trials and success probability 0.4, say what dbinom(3, size = 10, prob = 0.4) and pbinom(3, size = 10, prob = 0.4) return.
Why is the first of those not the probability of an interval?
Worked answer
dbinom returns the probability mass at the single point 3. For a discrete distribution that mass is the probability of one value, not of a range of values. pbinom returns the cumulative probability of 3 or fewer successes. An interval, such as the probability of 2, 3, 4, or 5 successes, is a difference of cumulative probabilities, or a sum of point masses. It is not one call to dbinom. The quantile function qbinom inverts the cumulative probability. It does not invert the height of the mass function.