I'm reading An Introduction to Ordinary Differential Equations by Agarwal and O'Regan. On page 28, I have the expression
$$y\left(x\right)=c\exp\left(-\int^x{p\left(t\right)\, dt} \right)$$
which is equation 5.4.
My problem is the missing lower limit of integration. I don't understand what the notation means. The context of the equation is solving the homogenous equation
$$y^\prime+p\left(x\right)y=0.$$
This leads to
$$\frac{y^\prime}{y}+p\left(x\right)=0.$$
The text says that by integrating both sides, we get the expression that is puzzling me. Any advice on how to interpret this notation would be appreciated.