Help with some maths problems please

The unit I'm doing at the moment is differentiation/integration and I have a few problems I'm having trouble with any help/tips are appreciated.

1) The velocity of a vehichle follows the equation y=6t+3 ms^-1

Using calculus determine the distance travelled by the vehicle between t=1 seconds and t=4 seconds.

2) determine the area under the waveform y=2sinX + 2cosX between x=0 and x=pi radians.

1) The equation to use is distance = integral(from t=1 to 4) v(t) dt where v(t) = 6t + 3.

So distance = (6*t^2 / 2 + 3t) = 3t(t + 1) evaluated from t=1 to t=4 which comes out to

3*4*(4+1) - 3*1*(1+1) = 60 - 6 = 54 m.

2) The area will be integral(x=0 to pi) (2sin(x) + 2cos(x)) dx = 2(-cos(x) + sin(x)) from x=0 to pi

= 2(-cos(pi) + sin(pi)) - 2(-cos(0) + sin(0)) = 2(-1) - 2(-1) = 4.

1) is integration, because the area under the line on a velocity/time graph is displacement:
3t^2 + 3x
Then substitute 1 and minus it off substituted 4:
(16 x 3 + 12 - (3 + 3)) = 54m

2) You need to use the trig identities, but I'm revising for my chemistry exam before I have maths C2, so really don't have time, sorry!

1) what are m and s?

2) Area = ∫[0,π] (2Sin(x) + 2Cos(x))dx = 2(-Cos(x) + Sin(x)) over [0,π]

= 2(-Cos(π) + Sin(π)) – 2(-Cos(0) + Sin(0))

= 2(-(-1) + 0) – 2(-(1) – 0) = 2(1) – 2(-1) = 4

never been good with math