Definite integration help

I forgot how to do these please help and show work!
a.) integral from 1 to x of (sint)^2
b.) integral from 5 to 3x of (t^2-t)
c.) integral from 0 to x^2 of abs(t)

a)
∫ sin^2 t dt
= (1/2) ∫ (1 - cos2t) dt
= (1/2) [t - (1/2)sin2t] + c
Plugging limits x = 1 to x,
= (1/2) [x - (1/2) sin2x - 1 + (1/2)sin2].

b)
Integration of t^2 - t w.r.t. t,
= (1/3) t^3 - t^2/2
Plugging limits t = 5 to 3x
= 9x^3 - (9/2)x^2 - 125/3 + 25/2
= 9x^3 - (9/2)x^2 - 175/6.

c)
For t = 0 to x^2 l t l = t
integrating t w.r.t. t,
= t^2/2 + c
plugging limits t = 0 to x^2,
= x^4/2.

The x's are just the upper bound of the integral. Evaluate t with that value the same as if there were a number there. Your answer will have the variable x in it but not t.

For example, the integral from 1 to x of t^2 is:
x^3/3 - 1/3

If you're having trouble with the integration:
a) Use the double-angle formula (sin t)^2 = (1 - cos(2t))/2
b) that's just a polynomial, you should know how to integrate it
c) 0 and x^2 are both ≥0, so within the entire range |t| is the same as t.

The definite integral of a function f(x) from a to b, where F(x) is any antiderivative of f(x) is:

F(b)-F(a)

So:

a. sint^2=1/2(1-cos2x), F(x)=1/2(x-1/2sinx), F(b)-F(a)=1/2(x-1/2sinx)-1/2(1-1/2sin(1)…

b.F(x)=1/3t^3-1/2t^2, F(b)-F(a)=9x^3-9/2x^2-(125/3-25/2)

c.Since its from 0-x^2, F(x)=1/2x^2, F(b)-F(a)=1/2x^4

Although it doesn't make sense why these would be the problems. Are you sure you weren't supposed to take the derrivative of the integrals or something?