I want to know the meaning of Semidefinite Integral.
I am used to read definite and indefinite integral but I want to know the meaning of such equation :
$\pi(e)\left(1-F\left[-\frac{a}{\pi(e)}\right]\right) \left(a+\frac{\int_{-\frac{a}{\pi(e)}}\mu f(\mu)d\mu }{\left(1-F\left[-\frac{a}{\pi(e)}\right]\right)}\right)$
Where :
$\pi(e):$ is the probability of finding the information $\mu$ depending of the effort $e$ of the agent. $\left(1-F\left[-\frac{a}{\pi(e)}\right]\right)$ is the condition for the agent to search this information depending on the parameter $a$ which can be viewed as a reward.
$\mu$ is a stochastic term distributed by $f(\mu)$, the expected value of $\mu$ is 0.
I do not understand the second term of the equation where there is only the lower bound: $\int_{-\frac{a}{\pi(e)}}\mu f(\mu)d\mu$