BIBO Stability

[Archduke Tips]

Does anybody know how to figure out if a system is BIBO stable or not?
I found through the internet that it can be done by taking the integral from -infinity to +infinity of the magnitude of the transfer function for continuous time systems, but I am pretty sure this is not the method that my teacher intends us to use.

It seems like he wants us to solve these problems by intuition... but I have only seen one example of a BIBO stable system and one example of an unstable system, and I have trouble applying them to the homework problems that are assigned.

For example here is one of the systems from the homework that I need to determine if it is BIBO stable or not:

y(t) = dx(t)/dt + x(t)

I don't even know where to start on this one because of the 1st order DE. It looks to me like it is BIBO stable, but I have no way to prove it.

Anybody know how to do this?