I am taking a linear systems and signals course and we are currently looking at system transfer function realization. The textbook states the following,
A transfer function \$H(s)\$ can be realized by using integrators or differentiators along with adders and multipliers. We avoid use of differentiators for practical reasons discussed in Sections 2.1. Hence, in our implementation, we shall use integrators along with scalar multipliers and adders. We are already familiar with representation of all these elements except the integrator. The integrator can be represented by a box with integral sign (time domain representation) or by a box with a transfer function \$\frac{1}{s}\$ (frequency domain representation).
I'm not entirely sure i understand why \$\frac{1}{s}\$ is the frequency domain representation for an integrator. When i hear the word integrator i'm thinking 'integration, finding the area underneath the curve, summing of areas...'. Could anyone explain to me why \$\frac{1}{s}\$ represents integration? I am not seeing the link.
Thanks in advance.