Difficulty understanding formula and area under v-t graph

1. The problem

For sake of format I attached the a screenshot of the course material I’m having difficulty wrapping my walnut around. Which is how:

Total Displacement = Area of Triangle + Area of Rectangle
or
Δvector d = Atriangle + ARectangle
or
Δvector d = 1/2 (V2-V1)Δt +V1*Δt

Translates in to:

Δvector d= 1/2 (V1+V2)Δt

Could someone explain it to me? I feel as if i’m blatantly missing an obvious answer as to why this is but since there is no answer in the text, I’m reaching out.

help.png contains screenshot
q.doc contains my question in better formatting

Attached Images
File Type: png help.png (74.9 KB)
Attached Files
File Type: doc q.doc (16.0 KB)

http://ift.tt/1fkZ9DY

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