The parseInt method might not always return expected results in some situations. For example the parseInt method converts to a string first and if it is a number the goes off into notation, then the letter e char will not be recognized as a number and will parse an int based on what comes before it.
There is also the nature of the max safe integer, when adding anything to that and going beyond the max safe int that too can result in unexpected results as well.
The Number function can be used to convert a string to a number also. It is a way to explicitly declare the the value that is given to the number function is th be parsed as a number. However it will not parse to an integer, at least not my itself, so it would have to be used in conjunction with an additional method such as the Math.round method.