is only defined for non-negative integers, you need something defined for all
reals in (0,n). Alternatively replace the integral with a summation from 0 to
n, which is 1 as you are summing the binomial distribution with parameters
n, p over all possible outcomes.
If the latter is the case, your original sum would heve been the mean of the
binomial distribution with probability of success on a single trial of p, and
a total of n trials, this is n*p.