# Integrate along the Curve

Calculus Level pending

Let $$N = \int_C ((x+yz)\ dx + 2x\ dy + xyz\ dz)$$, where $$C$$ is two line segments, one from $$(1,0,1)$$ to $$(2,3,1)$$ and another from $$(2,3,1)$$ to $$(2,5,2)$$. If $$N = \frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b$$?

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