Mathematical Science Analysis Supremum & Infimum

The infimum of the set \(\rm \left\{\int_a^b \sqrt{1+(y'(t)^2}dt:y \in C^1[a, b], \:\:\:\:\:y(a)=a^2, y(b)=b-5\right\}\) is

1
\(\rm \frac{19\sqrt2}{8}\)
2
19√2
3
\(\frac{19}{8}\)
4
\(\rm \frac{19}{2\sqrt2}\)

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