Answer
The graphs are not the same because the two given functions involve different transformations of the parent function $y=\sin{x}$.
Work Step by Step
The graph of the two given functions are different because they involve different transformations of the parent function $y=\sin{x}$.
The function $y=\sin{x} +1$ involves a vertical shift of one unit upward of the parent function while the function $y=\sin{(x+1)}$ involves a horizontal shift of $1$ unit to the left of the parent function .
