Find the Area Expression: Square with Side Length (x+1)

First, let's recall the formula for calculating the area of a square with side length y (length units):

$S_{\boxed{}}=y^2$Therefore, for a square with side length:

$x+1$ (length units), the expression for the area is:

$$$S_{\boxed{}}=(x+1)^2$Now, in order to simplify the expression, let's recall the perfect square binomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$Let's continue and apply this formula to the area expression we got:

$S_{\boxed{}}=(x+1)^2 \\ \downarrow\\ S_{\boxed{}}=x^2+2\cdot x\cdot 1+1\\ \boxed{ S_{\boxed{}}=x^2+2x+1}\\$This is the most simplified expression for the given square's area,

therefore the correct answer is answer D.