Your question is not clear at all.
When you say "under" the graph of
f(x) = 6x+1, the region would be infinitely large.
You will need to close it.
Is it bounded by the x-axis?
If so according to your interval part would be below the x-axis and part would be above it.
Make a graph to see what I mean, then clarify your question.
BTW, why would you need Calculus to find the area of a region bounded by straight lines?
Find the area of the region under the graph of the function f on the interval [-1, 2].
f(x) = 6x + 1
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