Computing an expectation with a uniform probability distribution.

Question

Suppose $F$ is a cumulative density function of a uniform distribution between $a=0$ and $b=B$ and $c$ is a positive real number.

I need to evaluate the integral $$\int_c^Bq\;\mathrm dF$$ where the integrand $q$ does not depend on the variable of integration that has the uniform distribution.

Is it the case that the answer to this problem is $\frac{B-c}Bq$.

I am pretty sure that the above is the correct answer, however when I use this answer in my main problem, I am getting counterintuitive results.

Thank you for your kind help!

Answer 1

Is it the case that the answer to this problem is [(B-c)/B]*q [?]

It is, but only when 0 < c < B. When c < 0, the result is q. When c > B, the result is 0.