Sending an int from C# to arduino that surpasses a bytes range.

You need to send a sequence of bytes containing your value. This means you need to decide on a message format. Your message format needs to make it possible to determine the start and end of each message. The simplest encoding scheme for this sort of data is to transfer it textually and use a text delimiter such as a linefeed to denote the end of the message. This means you need to format the number as a string on the sending side, and parse the string to obtain the number on the receiving side.

If bandwidth is an issue then sending the data in a binary format would result in smaller messages but then you need to deal with an encoding scheme that can contain arbitrary numbers - obviously, these could include any value you used to mark the start/end of the message so you the encoding scheme needs to be more complex.