I am trying to follow this proof on proof wiki https://proofwiki.org/wiki/Triangle_Inequality_for_Contour_Integrals
as I think the proof relates to a problem I am working on, however I do not understand the step
$$\displaystyle \sum_{i \mathop = 1}^n \int_{a_i}^{b_i} \left\vert{ f \left({\gamma_i \left({t}\right) }\right) }\right\vert \left\vert{ \gamma_i' \left({t}\right) }\right\vert \ \mathrm dt \leq \displaystyle \sum_{i \mathop = 1}^n \max_{t \mathop \in \left[{a_i\,.\,.\,b_i}\right] } \left\vert{ f \left({\gamma_i \left({t}\right) }\right) }\right\vert \int_{a_i}^{b_i} \left\vert{ \gamma_i' \left({t}\right) }\right\vert \ \mathrm dt$$
The reason given on proofwiki is Linear Combination of Integrals but I do not understand how that applies here.