$(4)[16$ pts$]$ Calculate the definite and indefinite integrals below $($a$)$ By finding the areas of geometric shapes. Z $5135+4$x $$ x $22|3$ x$|$ dx $($b$)$ By finding the most general antiderivative of the function. Z $($ x $1)($x $+2)2$ x $3/2+$ x $3+$ x $+3$ x $2+1$ sin x $2$ cos x $2$ dx