Problem $2$: Distance Travelled and Speed $(18$ points$)$

Directions: Suppose that an object moving along a straight line has position function s$($t$)=$ e$^(1$t$)*(2$t$^211$t $+14),$ measured

in feet, and velocity function v $($t$)=$e$^(1$t$)*(2$t$^215$t $+25),$ measured in feet per minute. The variable t is measured in

minutes. Use these functions to solve the following problems. Do not simplify your answers.

a$)(14$ points$)$ Write a definite integral that gives the total distance traveled of the object during the time interval $[1,4].$

Then calculate the distance traveled.