Not. Both are diferent.
The displacement from time t = 0 to time t = π is given by:
[tex]{\displaystyle s = \int _0^{\pi }4\cos\left(t\right)\:dt}[/tex]
[tex]{\displaystyle s = 4\left[\sin \left(t\right)\right]^{\pi }_0}[/tex]
[tex]s = 4[0 - 0 ][/tex]
[tex]s = 0[/tex]
The distance from time t = 0 to time t = π is:
[tex]{\displaystyle d = \int _0^{\pi }|4\cos\left(t\right)|\:dt}[/tex]
[tex]{\displaystyle d = \int _0^{\frac{\pi }{2}}4\cos \left(t\right)dt+\int _{\frac{\pi }{2}}^{\pi }-4\cos \left(t\right)dt}[/tex]
[tex]d = 4\left[\sin \left(t\right)\right]^{\frac{\pi}{2}}_0 - 4\left[\sin \left(t\right)\right]^{\pi}_{\frac{\pi}{2}}[/tex]
[tex]d = 4 + 4[/tex]
[tex]d = 8[/tex]
