If x is an internal angle of a triangle, then what is the range of the function y = SiNx + cosx? Why 45

If x is an internal angle of a triangle, then what is the range of the function y = SiNx + cosx? Why 45

y=√2sin（x+45）
If x is the internal angle, then 0 < x < 180
45＜x+45＜225
-√2/2＜sin（x+45)≤1
-1 ＜y≤√2
Draw a unit circle in the rectangular coordinate system, change from 0 to 360 degrees, 45 to 225 degrees, 90 degrees to the maximum value of 1, you can get it, 225 degrees to the minimum value - √ 2 / 2, but can't get it, look at the unit circle, image memory must remember hard back is much more useful
It's time to go,

∫sinx/(1+sinx) dx=?
If you can't do it for a long time, please help me,

The original formula = ∫ sinxdx + ∫ (1-cos2x) / 2DX
=-cos x+1/2*x-1/2∫cos2xdx
=-cosx+1/2*x-1/4sin2x+C

Calculate ∫ (- 1,1) x ^ 2 (1 + √ (1 + x ^ 2) SiNx) DX
Calculate ∫ (- 1,1) (x ^ 2) * (1 + √ (1 + x ^ 2) SiNx) DX
The original formula = 2 ∫ (0,1) x ^ 2DX = 2 / 3 why?

f(x) = x^2.√(1+x^2)sinx
f(-x) = -f(x)
∫(-1->1)(x^2)*(1+√(1+x^2)sinx)dx
=∫(-1->1)x^2dx
=(1/3)[x^3]|(-1->1)
=2/3