选C 6
y=(sin²x+1)(cos²x+3)=sin²xcos²x+3sin²x+cos²x+3=sin²xcos²x+2sin²x+4=sin²x(1-sin²x)+2sin²x+4
=-sin^4x+3sin²x+4=25/4-(sin^4x-3sin²x+9/4)=25/4-(3/2-sin²x)²