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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