37.
\(y=cos^2x+sinx+1\)
\(=1-sin^2x+sinx+1\)
\(=-sin^2x+sinx+2\in\left[0;\dfrac{9}{4}\right]\)
\(\Rightarrow T=\left\{0;1;2\right\}\)
\(\Rightarrow S_T=0+1+2=3\)
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