Use geometry to evaluate the following integral.

Integral from $1$ to $5$ f left parenthesis x right parenthesis dx$15$f$($x$)$dx$,$

where

$$f$($x$)$equals$=$left brace Start $2$ By $2$ Matrix $1$st Row $1$st Column $2$ x $2$nd Column if $1$ less than or equals x less than or equals $22$nd Row $1$st Column $7$ minus $2$ x $2$nd Column if $2$ less than x less than or equals $5$ EndMatrix

$2$x$$if$1$x$272$x$$if$2$