2 types of Line integrals in scalar field

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Consider the line integral,

$\int _ c$f(x,y)$\vec dr$ , where f(x,y) is a scalar field, and it is evaluvated on a curve c . After integration we get a vector let it be $\vec I$ .

$\int _ c$f(x,y)$\ dr$ , hear differential element is a scalar ( magnitude of $\vec dr$ ) , After integration we get a scalar, Let it be K , As usually I think

|$\vec I$| = K ,

But most of the cases it is not true, Can u please clear my concept ?