I Successive Integrals: Examining 1st Integral y_1(t)

[SuperCat]

My textbook shows the following example of successive integrals:

Does the 1st integral y_1(t) have a typo? Shouldn't the integral be taken with regards to Tau?
If not, I would appreciate an explanation of why the 1st successive integral is taken with regards to t, but in the second it is taken with regards to Tau.

 

[Mark44]

My textbook shows the following example of successive integrals:

Does the 1st integral y_1(t) have a typo? Shouldn't the integral be taken with regards to Tau?
If not, I would appreciate an explanation of why the 1st successive integral is taken with regards to t, but in the second it is taken with regards to Tau.

I believe you're right about this being a typo.
The integral should be $\int_{-\infty}^t y(\tau) d\tau$.

 

[SuperCat]

Mark thank you for your reply. I had a feeling that it didn't make sense, but I always feel a lot more comfortable getting a second opinion. This is now resolved.